If a and b are the non-zero distinct roots of $x^{2} + a x + b = 0$ , then the least value of $x^{2} + a x + b$ is

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Solution

The correct option is C -
Solution : a and b are root of $x^{2} + a x + b = 0$
Sum of root : $a + b = - a, 2 a + b = 0$
Product of root : $a b = b, b (a - 1) = 0$
${\begin{matrix} a = 1 b = - 2 & b \neq 0 \end{matrix}$
Minimum value of $x^{2} + a x + b$ at $x = \frac{- a}{2} = \frac{- 1}{2}$
$\equiv \frac{1}{4} + (- \frac{1}{2}) - 2 = \frac{- 9}{4}$

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