Q51 / 160 · AP EAMCET 2022 (04 Jul Shift 2) · Mathematics

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

A
$2$
B
$1$
Correct answer
C
$- 1$
D
$- 2$

Solution

Given:
$f (x) = x^{2} + a x + b$
$\Rightarrow f (0) = b$
So,
$f (f (0)) = f (b) = 0$
$\Rightarrow b^{2} + a b + b = 0$
$\Rightarrow b (b + a + 1) = 0$
$\Rightarrow b + a + 1 = 0$
$[∵ b \neq 0]$
$\Rightarrow a + b = - 1$

Hence, the correct answer is option: 'C'.

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