CAT 2025 Slot 1 Algebra Question Made Easy by Arun Sharma

Ajouté : 2026-05-18

[00:00:00]Difficult Quant Questions, Easy Solutions, Let's have a look. Question says that there are two quadratic functions fx gx whose minimum value is greater than the maximum value of g(x).

[00:00:08]So here the theory you need to know is that for any quadratic function ax² + bx + c the minima or the maxima happen at a value of x such as -b / 2a if I apply this principle on the first function what I will get is -b / 2a for this function is p is -4c so -b / 2a for this function a is one the value of x comes out is 2c and when we replace x / 2c in this equation we will get the minimum value of this function. And the minimum value of this function is just by replacing x by 2C.

[00:00:46]This will become 4C² this is - 4c * 2C which is - 8C² + 8C. Now we have to apply the same principle to the second function and for this -b / 2a. B is 3c here and a is -1.

[00:01:03]So -b - 3c / 2a which is -2. will give me the value of X as 1.5C at which the maximum of this function happens. So when I apply this in this expression the expression I get is 2.25² + 4.5 C² - 2C and this is the maximum value of this function. This minimum is greater than this maximum. So I have this equation -2.25C² should be smaller. When I apply this inequality that this expression has to be greater that this expression according to the question. I get this inequality and in which if we take the like terms aside - 2c will go there. So 10C is greater. So both these terms came here. And we will take c² on this side. So here we're getting 2.25 c². getting -4c². So + 4c² will come out. Which looks like 10C is greater than 6.25C².

[00:02:08]And the question is asking a possible value for C at which this is satisfied.

[00:02:13]And the values ​​given r to -2/2 and - 1/2. So if I apply to pay and see 20 greater than 6.25 * 4 25 not true. If I apply it on -2 then it will become a negative value here. A negative value cannot be greater than a positive value.

[00:02:32]So -2 and - 1/2 is also gone because of the same logic. If I use half here, then 10C is five and 6.25 C² is 6.25 * 1/4 which is obviously smaller than this five.

[00:02:47]And here the correct answer is half. Follow me for more. If you're looking for a cat coaching program and want to get personally tutored and mentored by me, do check out Mind Works.