Quadratic Equation Exercise 2a (All Questions) One Shot 🔥 | Class 10 Math Odia Medium

Added: 2026-05-24

[00:00:00]So hello everyone welcome to 2.0.

[00:00:26]Okay. Important exercise.

[00:00:34]So exercise for x² - 4x + 4 = 0 B² - 4 A C B - 4 - 4 row square - 4 into A 1 C 4 - 16US Basic concept.

[00:01:49]Okay.

[00:02:02]First question.

[00:02:05]Second question number x² - 5 x + d² - 4 a b - 5² - 4 into a C min 6 25us a clear question Number three.

[00:03:05]A x² a x² + b xus a.

[00:03:17]Okay.

[00:03:28]Alsign.

[00:04:04]by C. Okayus by A.

[00:04:15]Okay.

[00:04:16]Next question number five.

[00:04:30]Okay.

[00:04:36]For x² alpha + beta into x plus okay x² betaus - 1 -1 okay next x into x into next x² - x next - a x²us a= 0 x² + 1= Next question number six.

[00:05:46]Okay.

[00:05:56]Okay.

[00:06:04]for b² - 4 a c. Okay.

[00:06:22]square.

[00:06:31]Okay.

[00:06:35]Okay.

[00:06:44]minus 4 into a 1.

[00:07:01]Okay.

[00:07:09]Okay.

[00:07:16]- 3x 3x² - 2x - alus b by a minus 2 Okay. Next number 3x² - 2x - 1 = 0 by a Cus Aswus 1 by 3 question number. Okay.

[00:08:26]Question number three.

[00:08:38]US x² - ala + beta into x plus alpha beta= 0 x² beta - x + beta - 5 = 0. Next x² 3 - 5 - 2 - 2us - 2x - Okay.

[00:09:34]Question number two.

[00:09:43]M x² - 2x + 2 mus = 0.

[00:09:54]Okay.

[00:10:00]going to follow C by A.

[00:10:25]Okay. 3 m = 2 m -1 next 3 musc number x²us PX + 2= X²us P into X + 2= Next 6US 2 P = 0. Next 6 = 2 + 2 P= 6 by 2 6 by 2= Okay.

[00:11:49]Sorry. Number four.

[00:12:01]Question number four. X² - 2X + C= Dal D for B² C = B X - 2² - 4 into A 4 C next - 2² + 4us - 16 C = 0 next 4 = - 16 C + 16 C next C by 16 by 16.

[00:13:14]Okay.

[00:13:18]Question number.

[00:13:29]Okay. Next question number five.

[00:13:34]Question number five.

[00:13:37]5 x² + 2x 5 into square + 2 into x - 2 + k = 0. Next square plus 16= Okayus.

[00:14:30]Next question number number x² - k into x + = 0 6 = 0. - 3k 9 + 6 15 + 15 = 0. Next= 15 by 3.

[00:15:20]Okay.

[00:15:24]Number seven. Question number seven.

[00:15:33]2x² + k x + 3 = 0.

[00:15:51]B² - 4 B K² - 4 into A 2 C Next 24 = 0 Next K² = + 24 - 24= 2<unk> 6 question Question number three.

[00:16:52]X-ray.

[00:17:08]Option A. Answer.

[00:17:24]square x² into x² x ^ 4. Next square cancel x² into x answer.

[00:17:58]Next number 7 x² - 9 x + 2= 0 for b² - 4 a next - 9 - 9 row square - 4 into A 7 8 Okay. - 56 25t.

[00:19:10]meaning first option A. Okay.

[00:19:30]Okay.

[00:19:33]Answer question number 6 + 8= Als x + X into X - 8 = 0.

[00:20:37]Next question number four.

[00:20:53]C by A Cus Aswus by 3 option D answer. Okay. Next. Next question number.

[00:21:20]Question number five.

[00:21:23]4x² - 2x + 1= 0us b by a minus bus a 2x 1 by 2 answer okay answer option c option c 1 by two say next question number six question Number six beta minus b by a minus c by a c co A four 7 by 4 1 plus 1 by beta beta beta 1 beta beta beta alpha into 1 alpha alus 3x 4 - 3x 4 7 by 4 Next step by 4 by 7 - 3 by 7. Okayus by 7 option answer. Okay number next.

[00:23:21]Okay.

[00:23:28]x² + x² - beta into x plus alpha beta = 0 x² - beta 5= 2 into x² - 8 x + 2 x² - 8 x + 5 = 0.

[00:24:06]Okay.

[00:24:07]2x² - 8 x + 5. Okay. Answer option C.

[00:24:13]Option B. 2x² - 8 x + 5= question number four.

[00:24:31]Okay. First question number x² x² + x - 6 = 0 x² + x - A + B whole square A + B square A² + 2 A B + B square X² + 2 into A X + 2 into A 1 by 2.

[00:25:39]Okay. A square + 2 A square B square right side B square B square right side right Right.

[00:26:15]Left side a square + 2 a + b square x + 1 by 2 a + square. Okay. Say = 6 + 1 square 1 2 4 x + 1 by 2 1 by 2.

[00:27:01]Next next = 1x - 1x2 plus or minus 5x2 5 by 2. Next= -1 by 2 + 5 - 5 by 2 - Okay, - 5 - 6 by 2 - Good answer.

[00:28:03]number one. Next question number 2x² x + 4 = 0 2x² - 9 x + 4. Next.

[00:28:39]2x² by 2 - 9 by 2 = -4 by 2.

[00:28:59]Okay.

[00:29:09]A whole square - 2 a + b square x² - 2 into a x 9 by 4. See 9 by 9.

[00:29:45]Next square= - 2 9 by 4 row square A² - 2 A + B square A whole square A X B 9 by 4 A - B square = - 2 + square A Next x - 9x 4 x - 9 by 4 = square root 81. Next x - 9 by 4 32 49 49 49 Next = 9 by 4 + 7 by 4 9 by 4 - 7 by 4.

[00:31:54]Question number two.

[00:31:56]Question number three. Question number three.

[00:32:01]14² + 14² + next. Next 14 + x by 14 = 3x4.

[00:32:25]Next 14 14 cancel x² + 2 into a x 1 by 1 into Okay. 1x 28.

[00:32:58]Next 1x 28 square left side 1x 28 row square= 8 3x 14 + 1 by 28 row square. Okay.

[00:33:14]A + B square I square + 2 A + B square A + B 1X 28 square= 3 by 14 + 1 square 1 square 8 7 784 78 84. Okay.

[00:33:46]Next. X + 1 by 28= 7 84 7 84.

[00:34:06]Next 568.

[00:34:19]Next 784 784.

[00:34:26]Next step x + 1 by 28 = 169 168 + 1 169 169 134 28 28us Okayus age x = -1 by 28 plus or minus 13 by 28 13 by 28 x= - 1 by 28 + 13 by 28 next - 1 by 28 - 13 by 28 28 28 28us 28us - 12 by -4 by 28 by 3 by 7 - 1 by 2. Answer number four.

[00:36:02]Question number four.

[00:36:06]3 x².

[00:36:08]Question number four. 3x² - 32x + 12 = 0. First 3x² - 32x = next.

[00:36:23]3x² by 3 - 32x 3 = -2 by 3 x² - 32 x 3 a² - 2 into a Okay.

[00:36:59]16 by 3. Next square= - 4 + 16 by 3 row square. Okay.

[00:37:15]A - X - B 16 by 3 to A - B² = - 4 + 16 square next 3 Okay.

[00:38:05]Next. X = 16 by 3 plus or minus <unk>2= 16 by3 + <unk>2 by 3 16 by3us<unk> 220 by 3 <unk>220us <unk>220 Okay.

[00:38:49]<unk>220. Okay. 1x3 into 16 - <unk>220.

[00:38:56]Answer. Okay.

[00:39:01]Question number four.

[00:39:04]Question number x² x² + 2 px - 3 qx - 6 = x² equal to a - 6 p + 6 pq + 6 pq 2 pus 3q 2 P - 3 Q by 2 row² 6 P 2 P - 3 Q by 2 row square okay a - X + B 2 P - 3 Q by 2 A + B² equal to 6 P Q + 2 P - 3 Q².

[00:40:39]Next x + 2 p - 3 q by 2 square plus 2 p - 3q square. Okay. Next x + 2 p - 3 q by 2.

[00:41:06]root 2 pus 3 square 24 into a 2 A B A whole square + 4. Okay. A - square + 4 A + B² next X + X + 2 P - 3 Q 2 P - 3 Q by 2 = A whole square + 4 A + B square A 2 P 2 P B 3 + 2 P - 3 Q by 2= plus or minus square root 2 P.

[00:42:49]Okay.

[00:42:58]Okay.

[00:43:13]- 2 + 3 by 2 plus 2 P + 3 Q by 2 - 2 P + 3 Q + 2 P + 3 Q + 2 P - 2 P 3 Q + 3 Q 6 Okay.

[00:43:45]Next. X = - 2 P - 3 Q by 2 2 P - 3 Q by 2 minus 2 2 P + 3 Q by 2 2 P + 3 Q by 2 - 2 P - + 3 Q - 2 P - 3 + 3 - 3 - 2 P - 2 P - 4 P by 2 minus 2 P okay 3 question number okay five numbers Question number six <unk>3 x² + 10 x + 8<unk>3 = 0. Okay.

[00:45:01]<unk>3 x² + 10 x= - 8<unk>3 roo<unk>3 I <unk>3 = - 8= -8² + 2 into a x b simple 5 roo<unk>3 next square.

[00:45:51]Okay.

[00:45:52]5 <unk>3 square a + square a x + b<unk>3 square= roo<unk>3.

[00:46:09]So next x + 5 by <unk>3= square root.

[00:46:23]Next x = x = 5<unk>3.

[00:46:46]Okay.

[00:46:49]Plus x = - 5 by<unk>3 + 1x<unk>3 - 5 by<unk>3 - 1 by<unk>3 roo<unk>3 roo<unk>3 roo<unk>3 cancel - 5 + 1 roo<unk>3 - 5 - 1 - 4 by<unk>3 - 6 by<unk>3 - 4 by<unk>3 - 6 by<unk>3 roo<unk>3<unk>3 - 4<unk>3 into roo<unk>3 roo<unk>3 into roo<unk>3 into roo<unk>3<unk>3 roo<unk>3 into roo<unk>3 question number Question number seven.

[00:48:12]25 x² + 30 x.

[00:48:20]Okay. 25.

[00:48:24]Okay.

[00:48:31]X² + 6 X by 5 - 7 by 25 X² A² + 2 into A X B 3x 5 square 3x 5 square - 7 25 + 3x 5 row square. Okay.

[00:49:05]A + square + 3x 5² = - 7 by 25 square.

[00:49:17]Next + 3x 5.

[00:49:28]Okay. Next.

[00:49:32]X= + 3x 5 - 3x 5 x = - 3x 5 plus 92 x = - 3x 5 + <unk>2x 5 say - 3x 5 - <unk>2 by 5 - 3 + <unk>2<unk>2 answer number 3 a² x² + 8 a b x + 4 b² equal to okay 3² x² + 8 a x = - 4 b² next 3 a square okay by 3 a² by 3 a² by 3 a² square x² bx 3 a = - 4 b² by 3 a² x² + 2 a 2 into a x into a 82 B square 4 B by 3 A² plus A plus= - 4 B² A 3 A square A + 4 B by 3 A square.

[00:52:00]Okay.

[00:52:02]A - X + B 4 B by 3 A whole square equal to A - 4 B² by 3 A² + square 16 B square by square 9 A² 9 A square Okay next square X + X + 4 B by 3 A =<unk> / of<unk> of - 4 B² by 3 A² - 4 B² by 3 A² + 16 B² + 16 B² by 9 A² okay - 4 B by 3 A plus or minus Okay plus or minus a square. Okay.

[00:53:11]- 12 b² - 12 b square + 8 a square 16 16 b square. Okay.

[00:53:22]x = - 4 b by 3 a plus or minus. B square A square. Okay.

[00:53:38]X = - 4 B by 3 A plus actually.

[00:53:55]Okay. Next plus 2 B by 3 A next - 4 B by 3 A - 2 B by 3 A loss 3 A - 4 B + 2 B A loss 3 A - 4 B - 2 - 4 B + 2 B - 2 B by 3 A - 4 B - 2 B - 6 B by 3 A - 2 B by A good answer okay number X² + A= B Next a + square x² into a x cancel a b square a 2 square= b a by 2 square. Okay.

[00:55:26]A square + 2 a + b square. The formula a x + b a by 2 a + b whole square. Okay.

[00:55:35]Next minus b + a² a² by 2 square.

[00:55:41]Next by 2= - 4 b a square x + a by 2 = a² plus - a by 2 plus or minus plus or minus roo<unk> a² - 4 b 2 by 2 plus x = - a by 2 + roo<unk> of A square - 4 B by 2 A + roo<unk> of A² B= A by 2 roo<unk> of A² - 4 B by 2 AUS roo<unk> of A² - x² + b x= a² already x² + 2 into a b square b² = 8 a² - a + b by 2 square x a b / 2 a + squareal A square + b square.

[00:58:14]Next x + b by 2 row square= 4 a² minus 4 a + 4 cancel b² x + b by 2 row square= 4 a² a square into a 2 a Next b² next x + b by 2 x + b by 2 = square root. Okay.

[00:59:13]A square for a minus b square A 2 A minus B 2 A square Bus by 2 plus it Okay. - b by 2 + 2 a - b by 2 - b by 2 - 2 a - b by 2 - b + 2 a - bracket - 2 a - 2 a by 2 - a - 2 a - plus next 2 a b 2 a b A by Okay.

[01:00:59]Okay.

[01:01:02]A minus. Okay. A minus Bus Ache.

[01:01:30]Okay.

[01:01:35]= roo<unk> b square by 2 a 4x² - 11 x + 11 c= - plus or minus roo<unk> of b² - 4 a c by 2 a minus b - 11 plus or minus roo<unk> of b - 11 - 11 b² - 4 into a 4 c 2 into a 2 into a - 96 by next orus 96 25 by 8 plus or minus Okay.

[01:03:18]Okay.

[01:03:23]Very simple.

[01:03:30]Question number two.

[01:03:37]Question number two into x= 0.

[01:03:46]- 1 2x into x - 2 -1 into x - 2 = 0 2x into x 2x² 2x into 2 4x - 1 into x - x - 2x² - 4x - x - 5 x + 2 = 0 1 2 c x = - b + or - b² - 4 a 0<unk> / by 2 a - 5 + or - b² b square - 5 row square - 5 row² square - 4 into a 2 c 2 by 2 into a 2 into a a 2 - plus 5 plus or minus - - 5 squareus.

[01:05:09]Okay.

[01:05:16]= x = 5 + 3x 4 5 - 3 by 4 5 + 3 8 Okay.

[01:05:54]Next page. Okay.

[01:05:57]Question number three number x² - 1 + <unk>2 into x + <unk>2 = 0 x² into 1 +<unk>2 for x = b + or minus<unk> b² - 4 a c by 2 a x = 1 + <unk>2 okay into 1 +<unk>2 plus b²us into 1 +<unk>2 square okay square - 4 into a 1 C<unk> 2 by 2 A 2 into A 1 Next X = 30 - - 1 + <unk>2 plus or minus square root of 1 + <unk>2² - 4 into 1 into <unk>2 by 2 next X = 1 +<unk>2 same 1 +<unk>2 plus notice roo<unk>2 A + B whole square - 4 A B A + B square A whole square - 4 A b square. Okay. A 1 -<unk>2 square roo<unk>2 a + square for a b square.

[01:08:13]Next x = 1 + <unk>2 plus or minus square root 1 -<unk>2 by 2 by two 1 + <unk>2 plus 1 - <unk>2 by 2 next 1 + <unk>2us 1 -<unk>2 by 2 cancel 1 + 1 2 2 by 2 1 - 1 - 1 -<unk>2 + roo<unk>2 2<unk>2 by 2 2 Question number four.

[01:09:10]Next question.

[01:09:12]Question number four.

[01:09:15]A into x² + 1 = x into a² + 1. Okay.

[01:09:23]A x² + a into 1 a= a square + 1 into x.

[01:09:35]Next a x²us a square + 1 into xal into a square + 1 a formula.

[01:10:05]X = - B plus or minus<unk> B² - 4 A C by 2 A to - Bus into a square + a² + 1.

[01:10:24]Next plus or minus b square into a square + 1 square a square + 1 square next a c I by 2 A by 2 A. Next.

[01:10:59]Next.

[01:11:01]Next. X = X = a A² + 1. A² + 1. Next orus. Not this A square B a A + B square - 4 A into a square a square + 1 square into a - a² into 1 4 into a into a 4 a² okay 4 into a² into 1 square A + B square - 4 A B 1 square Okay = A² + 1 into plus or minus a² - 1 square a whole square a whole square by 2 a next = roo<unk> square - 1 by 2 a square Plus a square + 1 - 1 cancel x= a square + a square 2 a square a cancel x= a into a square.

[01:13:01]Okay.

[01:13:04]A square + 1 - A square - 1 A square 1 2 A sorry 1 + 1 2 1 2 2 by 2 a 1 by a Okay 1 by a question number four question number Question number 51. Next page number 6 x² + 11 x + 3 = 0 11 c x for -<unk> / b square - 4 a c by 2 a minus b plus or minus b square - 4 into a 6 into c 3 by 2 a 2 into a 6 - 11 plus next = -1 plus or minus - 11 plus or minus 49 by 12. Next x = x = 11 plus x = a plus byus = a Okay.

[01:15:37]- 3 by 2. Okay.

[01:15:42]3us 3 by 2.

[01:15:46]Question number five.

[01:15:48]Question number six.

[01:15:50]Question number six.

[01:15:53]Question number six. 2x² + 41 xus = 0. A 2 b 41 cus.

[01:16:07]x = -<unk> / b² - 4 a c by 2 a. A x = - b 41 + or minus b square 41 row square - 4 into a 2 cus by 2 a 2 into a 2 - 41 plus or minus square.

[01:16:42]Okay.

[01:16:48]Next.

[01:16:50]Next.

[01:17:17]Next.

[01:17:21]X = - 41 - 41 plus or minus Okay.

[01:17:54]Next.

[01:18:14]Next. Next.

[01:18:27]51 x = - 41 plus or minus 51 by 4. Next x = -41 + 51 by 4. Say - 41 - 51 by 4. Next = 10 by 4 by 2us 90 92 92us 23 Okay. Answer 523 question number seven question 12 x² + x - 6= 0 a bar a cus to x formula - plus or minus roo<unk> b² - 4 a c 2 a - b a plus or minus b square a square a - 4 into a cus 2 into a bar -1 plus or minus 1 Minus minus next step x = -1 plus or minus orus + x= -1 + 17 by 24 -1 - 17 by 24 x= Okay.

[01:20:58]2x3us 3x 4 2x 3 - 3 by Okay.

[01:21:18]Question number seven. Question number 8.

[01:21:22]6 x + 5 into x - 2 = 0 = 0 6 x - 2 + 5 x - 2 = 6 into x 6 x²us.

[01:21:49]Next 6 x² - 12 + 5 - 7 x - 10 = 0. Okay.

[01:22:01]A b formula x = b plus or minus roo<unk> of b² - 4 a c by 2 a - b - 7 - 7 roo<unk> of b square - 4 into - 4 into a c minus also. Okay.

[01:22:37]Next.

[01:22:40]X = 7 + or - 7 plus or minus - - plus 49 + 240 by 12. Next = 7 orus 289 by 12. X = 7 + 289 17 by 12. Next plus x = 7 + 17 by 12 7 - 17 7 - 17 by 12 x= 24 24 by 12us us by 6. Okay.

[01:23:59]Question number 15² - x - 28 = 0. Okay.

[01:24:15]A 15 B -1 C - 28 C - 28 to formula X = - B plus or minus<unk> / B² - 4 A by 2 A by 2 A = B A plus or minus B square A - 4 into A C - 28 by 2 into A 2 into A 15 X 1 + 1 - - Okayus.

[01:25:18]Okay.

[01:25:25]Next 31 plus or minus.

[01:25:35]Next = 1 + 41 41. Okay.

[01:25:47]301= 1 + 41 by 30 1 - 41 by 30 42 by 30 - 40 by 30 by Okay.

[01:26:20]Three question number 10. Question number 10.

[01:26:29]Question number 10.

[01:26:31]X + 5 into X - 5 = 39.

[01:26:37]X + 5 into X - 5 A + B into AU. Formula A².

[01:26:45]Okay. = 39 x²us 39 = 0 x² 64 = 0 A - 64 x= root 64 plus or minus b² - 4 a c 2 a minus bas plus square into a 1 c4 - 64 by 2 into a a 1. Okay, plus 64 into 4 Fore Question number six.

[01:28:46]Question number six.

[01:29:01]for 12.

[01:29:30]12 x² - 13= 0. Okay.

[01:29:54]sustalus b a okay 12 alpha plus alpha 13 alpha 13= by a bus minus 13 by a four next Okay.

[01:30:44]1x4.

[01:30:58]Next 4 x² - 13 x + k = 0 4 into x 1 by 4 - 13 into x 1x = next 4 into 1 square okay next -3 by 4 + k = 0 1 by 4 - 13x 4 k = 0 next = 13 - 1 Okay. Next 13.

[01:32:02]Okay.

[01:32:10]Okay.

[01:32:12]forc.

[01:32:22]Next one by four. Next.

[01:32:36]Next.

[01:32:47]C by A= C by A= C by A 12 into 12 alpha square by A.

[01:33:10]Okay.

[01:33:11]12 into alpha alpha 1x 4 1x 4 square = kx 4 into 1 square= Okay.

[01:33:40]Okay. forcage insert.

[01:34:10]Next.

[01:34:23]Okay. Question number six.

[01:34:27]Question number seven.

[01:34:32]Question number x² - 5x + = 0.

[01:34:58]Okay.

[01:35:05]S ala + 3 alpha + 3 + b by a minus b by a plus ala 2 alpha plus 3= bus by a 1 2us 2 by2 same process.

[01:35:55]Okay.

[01:35:58]Follow C by A.

[01:36:17]1 into a 1 + 3.

[01:36:39]Okay.

[01:36:40]Question number eight.

[01:36:48]Question number 2² - 5 - by a minus b - 5 a 2 plus a square beta alpha beta square.

[01:37:41]Okay.

[01:37:46]Alsw 2x² - 6 + 3= plus by a minus b - 6 a 2 - c by a ca + 1 into beta + 1 beta Beta + 1 + 1 into 1 alpha beta + 1 into 1 1.

[01:38:59]Okay. Alsw 2x²us into P + 1 into X + P - 1 P - 1= 0 beta beta Both square A square A square A whole square A + B square A + B squareus - 4 a b 4 a b alpha - beta whole square alpha + beta whole square - 4 alpha beta equal to beta square okay by a 2 okay C by A C P Okay P + 1 by 2 square - 4 into alpha beta P -1 by 2 equal to alpha beta P -1 by 2 whole square. Next square minus P -1 by 2² equal to - 2 into P - 1 + 2 into P - 1 into A brow square by 2 square A + B by 2 square - A - B by square.

[01:42:19]Okay.

[01:42:26]A + B whole square minus A minus B A + B by 2 whole square - A minus B whole square for A B 1 P into 1= 2 P 2 into P - 1 P = 2 P - 2 into 1 2 Next 2 P P P P P P P P P P P P P P P P P P P P Pus P 2 = 2 Question number 11. Okay.

[01:43:12]Question number 11.

[01:43:20]5 x² - 3x - 2 = 0.

[01:43:27]beta.

[01:43:34]Okay.

[01:43:44]A C A plus B formula A + B - 3 A 3 A into B a + 3 a into a Okay 3x 5 into - 2x 5 - 2 by 5 into alpha + beta 3x 5 Okay.US plus 1 into 27 27.

[01:45:14]Okay. 11.

[01:45:19]Question number 12.

[01:45:33]+ a minus a c by a c.

[01:45:52]Okay.

[01:45:55]1x alpha square + 1 by beta square alpha square beta square alpha square alpha square cancel beta square into 1 h beta square beta square beta square cancel alpha square into 1 h alpha square a square + b square formula a + b² - 2 a okay alpha + beta square - 2 alpha beta see by by alpha square.

[01:46:29]Okay, that is a square + square into 6 by 6 by 5 square.

[01:46:53]Next square plus 289 square.

[01:47:03]Okay.

[01:47:05]Minus 12 by square by 36 x 5 36 by 56 by 25. Okay.

[01:47:35]289 36 by 25 25 289 to 60 229 229 by 36 229 by 36 cancel 11 number x² - 8 x + 16 = 0 by a minus b - 8 A 1 plus 8 - plus alpha beta C by A C 16 P by A 1 16 P alpha beta by alpha + beta alpha beta alpha beta 16 p 16 by alpha plus beta 2. Okay.

[01:48:57]Question number 13. Question number 2 into 5 + 2 m into x + 3 into 7 + 10 m = 0.

[01:49:23]for B² - 4 A= Next into 5 + 2 M - 2 into 5 + 2 M number square 3 into 7 + 10 m. C 3 into 7 + 10 m.

[01:50:08]Okay.

[01:50:12]Next square.

[01:50:21]Okay.

[01:50:23]+ 2.

[01:50:27]Next 21 mal square.

[01:50:50]Okay.

[01:50:52]A square plus a 2 into a - 5 B 2 M + B square 2 M² next + - 30 mal= Z Next 20 m 20 m² 4 m² - 21 - 30 m = 0 to next 4 m² 4 m² + 20 m - 30 m - 10 - 10 mus 2 m² next 10 Next.

[01:52:26]Okay.

[01:52:31]Next= 0.

[01:52:44]Okay.

[01:52:59]minus. Okay.

[01:53:18]Yes.

[01:53:21]2 m² - 4 m -1 m - 4 - 4 into -1 + 4. Next.

[01:53:44]Musal 2= 0. Next mus 2 =0. Say 2 mus 1 = 0 m = 2 mus 1 by 2. Okay.

[01:54:26]Skin question number x - a into x - B + X - B into X - C + X - C into X - A= 0al.

[01:55:18]Okay.

[01:55:20]X A next.

[01:55:26]Okay.

[01:55:28]X Okay.

[01:55:45]A X - A square.

[01:55:49]Next x - a into x - a square plus x - a square = 0. Next square= x²= next a whole square.

[01:56:20]A square x a² - 2 into a - x b a + b² a² = 0.

[01:56:31]Next. x²us 2 a x + a²= 0 x²us 2 a x + a² = 0 = b² - 4 a c x - 2 a - 2 a² - 4 into a 1 c a square 4 a square a First number question number Second 15 second a b a b c belongs to Okay. Basicceptal zero.

[01:58:41]A + B= C minus C.

[01:58:45]Bus A B + C - A into X² + C + A - B into X + A + B - C = 0 + C A bus into x² plus c + a + cus b into x.

[01:59:26]Next plus a + b a plus cus next - a - 2 a - 2 a x² - 2 b into x - 2 c= 0. Next.

[01:59:52]Okay.

[01:59:57]B x - c = 0. Next a x² + b x + c = 0.

[02:00:17]a x² + b x + c = 0. Okay.

[02:00:31]D for B square A B square - 4 A B square B square B square D square B square us a c a + cus a c. Okay.

[02:01:24]A a c a + square a + b² - 4 a - whole square for a whole square.

[02:01:50]Okay. A + square A whole square question number 15.

[02:02:22]Question number 16.

[02:02:25]Number 16.

[02:02:33]29.

[02:02:36]Okay.

[02:02:42]Okay.

[02:03:01]Sorry bet.

[02:03:15]Next square al square 29 a square a square a + square - 2 a alpha + beta whole square minus 2 alpha beta 29 square - 2 alpha beta = 29 next square noal + 2 alpha beta next - 29 - 20= = 2 alpha beta 2 beta next - 20 by 2 - 10 x² - beta into x cos = 0 x² + 3xusal answer question number 17.

[02:05:15]Okay.

[02:05:18]2x² - 4x + a - b - 4 by a 2 c by a c a by beta plus beta by alpha beta by alpha plus 4 into 1 by alpha + 1 by beta plus 2 alpha beta 2 beta beta Beta beta cancel alpha into alpha alpha square plus alpha alpha cancel beta into beta beta square plus 4 into alpha beta alpha alpha cancel beta beta beta cancel alpha beta square - 2 alpha beta a² square + b square formula a + b square - 2 a by alpha beta plus 4 into alpha + beta by alpha beta plus 2 alpha beta 2 into A by alpha beta alpha beta 11 alpha beta a plus 4 into alpha plus beta d by alpha beta a plus 2 into alpha beta next.

[02:07:47]Okay.

[02:07:50]Question number 17.

[02:07:52]Question number 18. Question number x² + b x + c = 0.

[02:08:17]Okay.

[02:08:36]sust by A minus B by A. Okay.

[02:09:00]Alpha= B by A. Next step by 5 by 5.

[02:09:13]Next.

[02:09:16]Next.

[02:09:27]A= C by A. Next.

[02:09:36]Next.

[02:09:38]Alpha into 4. 4 alpha square alpha square by a= c by a 4 into bal.

[02:10:00]Next 4 - square + b square + b square b square a square a square by a next a b square a b²= 25 a square c² = 25 a Okay.

[02:11:07]Next. Question number 18. Second.

[02:11:12]Second number.

[02:11:14]square - px plus q = equal to Z.

[02:11:38]Next minus by a + 2. Okay.

[02:11:57]US A 2 plus alpha 3= -3.

[02:12:11]Next.

[02:12:20]C by A.

[02:12:31]A 1. Okay. C A 1 2 Ala square= Q. Next 2 into alpha alpha P by 3. Okay. P by 3²= Q. Next 2 into P square P² by square= Q. Next 2 P² = 9 Q 9 Q 9 Q Okay.

[02:13:15]Okay. Question number 19.

[02:13:25]Okay. I'm 41 x² - 2 into 5 a + 4 b into x + a² + b²=al Next - 2 into 5 a + 4 b to² - 4 into a 41 c a² + b²= 0. Next square + d square. Next 5 a + 4 square - 2 square + next - 41 41 a² 41 a² + 41 b² = A square 5 a² + 2 a b 2 into 5 a into 4 b 2 a next b square nextus 4 s - 41 a² - + - 41 1 B².

[02:15:15]Okay.

[02:15:16]A zero. Next square 40 A plus square B²US 41 A²US 41 B²= 0. Next 41 a² + 25 a square - 16 a² - 16 a² next square - 25 b² 40 a 40 AB. Okay. + 40 A = Z.

[02:16:17]Next a square - 25 b² - 40 a = 0us 16 a square 4 a whole square 4 row square 25 square bin minus minus 40 a square into a 4 aales A square + square a - b - 5 b square= 0 next 4 a - next 4 a= 5 85.

[02:17:52]Okay.

[02:18:04]plus px + q = 0.

[02:18:27]Okay.

[02:18:35]Alpha beta square.

[02:18:56]Alpha + beta= alpha + beta= a square for a + alpha + beta square - 2 alpha beta minus 2 alpha beta aus c by A C A + Bus Pus Balus Pus² into Ala Q minus P= P² + P² square.

[02:19:55]Next square next 2.

[02:20:10]Okay.

[02:20:15]Okay.

[02:20:17]Second number.

[02:20:19]Third number.

[02:20:36]equal to Z.

[02:20:55]square alpha square by a square minus PS minus P. Next. Next.

[02:21:45]Ala square into Okay.

[02:22:03]- Alpha + Ala² = - P minus P Q + Q² + Q= 3 Both Alus A square root A + B + 3 A into A + BA square A Q + BA² + 3 A 3 into AA square into AA.

[02:23:12]Okay. AQ + B + 3 A into A= PQ.

[02:23:24]Next Y square.

[02:24:04]Next. Plus 3 into square into Okay. Next Pus Q + Q ² plus 3 PQ 3 PQ= minus PQ next Q² square pon sorry Okay, next.

[02:25:20]Okay, last question number 20. Last number into C² + B into C - A into X + C into A minus B= Okay for b² - 4 A = Bus A square - 4 into A² A into B - C into C into A minus Bal.

[02:26:21]Next bus square a into b minus c into c into a minus bal.

[02:26:39]Next bus c. Okay.

[02:26:59]4 into a into b minus c into a minus b = 0.

[02:27:10]US square bus square. Okay. - 4 into a into b minus c into c into a minus bal.

[02:27:33]Next.

[02:27:43]A minus BUS A plus AUS plus AUS B.

[02:27:54]Okay.

[02:28:01]A minus BC. A B - B 0² - 4 into 4 into A into B minus C. A into B minus C into C into A minus B equal to A.

[02:28:23]Next plus square plus a cus b into b minus c into c into a minus b.

[02:28:43]Okay.

[02:28:49]Bus whole square - 4 into A into B minus C C into A minus B = 0 A² - 4 into A into B A + B² - 4 A B Okay.

[02:29:38]A + B square - 4 A B A + B² - 4 A B A whole square A whole square A into B minus C into A minus B square= A + B square A formula A minus B square A whole square C minus A C - plus B C square + B A + B C A minus A C minus - 2 a= 2 a next.

[02:30:49]A B + B C A plus A + B C - 2 A plus 2 A A by A B C plus B C by A B C = 2 A by A B C 1 2 by 1 by A + 1 C= 2 B 1 by A + 1 by C = 2X B 2 by First part. Okay. First part next second.

[02:32:23]Okay. Thank you. Bye.