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 :
Explanation:
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.
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