CAT 2017 Slot 1 — QA Question 27
Discriminant and Roots of Quadratic EquationEasy
If f1(x) = x2 + 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 :
Answer & solution
Answer: 24
Solution
x2 + 11x + n = x
⇒ x2 + 10x + n = 0
For roots to be real and distinct, Discriminant > 0
⇒ D = (10)2 - 4 × 1 × n > 0
⇒ 4n < 100
⇒ n < 25
Therefore, highest possible integral value of n is 24.
Hence, 24.