# Quantitative Aptitude – Algebra – Functions – If f1(x) = x^2 + 11x + n

## Question

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

## Solution

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 – 4n > 0
On solving the inequality, we get, n<25 So, max positive integer value of n = 24. Answer: 24

## CAT 2017 Questions from Quantitative Aptitude – Algebra – Functions

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