Distinct Real Roots Condition

CAT 2017 Slot 1 · Quantitative Ability · Medium · Functions

This is a medium Quantitative Ability question from the CAT 2017 Slot 1 paper. It tests Functions. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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If $f_1(x) = x^2 + 11x + n$ and $f_2(x) = x$ , then the largest positive integer $n$ for which the equation $f_1(x) = f_2(x)$ has two distinct real roots, is:

Answer

Explanation

$f_1(x) = f_2(x) \implies x^2 + 11x + n = x \implies x^2 + 10x + n = 0$ . For two distinct real roots, discriminant $D > 0$ . $10^2 - 4n > 0 \implies 100 > 4n \implies n < 25$ . Largest positive integer $n$ is $24$ .

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Distinct Real Roots Condition

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