Question

If $f(f(0)) = 0$, where $f(x) = x^2 + ax + b$, $b \neq 0$, then $a + b =$

• A. $2$
• B. $1$
• C. $-1$
• D. $-2$

Hint:

Substitute expressions step-by-step to evaluate nested functions and use given conditions.

Answer 1

The Correct Option is C

Let $f(x) = x^2 + ax + b$
Then $f(0) = b$, so $f(f(0)) = f(b) = b^2 + ab + b$
Given $f(f(0)) = 0 \Rightarrow b^2 + ab + b = 0$
Factor: $b(b + a + 1) = 0$
Since $b \ne 0$, $b + a + 1 = 0 \Rightarrow a + b = -1$