Question

Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. If one of the roots of f(x) = 0 is –1, then the sum of the roots of f(x) = 0 is equal to:

• A. $\frac{11}{3}$
• B. $\frac{7}{3}$
• C. $\frac{13}{3}$
• D. $\frac{14}{3}$

Answer 1

The Correct Option is A

The correct answer is (A) : $\frac{11}{3}$
∵ x = –1 be the roots of f(x) = 0
∴ let f(x) = A(x + 1)(x – b) …(i)
Now, f(–2) + f(3) = 0
⇒ A[–1(–2 – b) + 4(3 – b)] = 0
b=14/3
∴ Second root of f(x) = 0 will be $\frac{14}{3}$.
∴ Sum of roots 
$=\frac{14}{3}−1=\frac{11}{3}$