If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is

24

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,

f1(x) = f2(x)

x^2 + 11x +n = x

x^2 + 10x + n =0

To have distinct and real roots, D>0

D = b^2-4ac = 100 â€“ 4n > 0

On solving the inequality, we get, n<25

So, max positive integer value of n = 24.

Answer: 24

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