CAT 2025 Linear and Quadratic Equations Question (Hard)

Question

If , then the sum of all real roots of the equation , is

Accepted Answer

Let x 2 3x be equal to k. We have, f x k k 2 k 2 2k Therefore, k 1 9701 We get k 9700. Thus, x 2 3x 9700 or x 2 3x-9700 0 Since x is real, the discriminant of the above quadratic has to be greater than or equal to zero. We find that 3 2 4 9700 geq 0 and therefore the quadratic has real roots. The su

CAT 2025

Quantitative

Linear and Quadratic Equations

Hard

If $f(x) = \left(x^2 + 3x\right)\left(x^2 + 3x + 2\right)$ , then the sum of all real roots of the equation $\sqrt{f(x) + 1} = 9701$ , is

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