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If $\alpha$ and $\beta$ are the roots ofthe equation $a x^{2}+b x+c=0$, where $a \neq 0$, then $(a \alpha+b)(a \beta+b)$ is equal to:
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The correct answer is:
$c$
Given equation $a x^{2}+b x+c=0 \quad$ (where $a \neq 0$ ) $\alpha$ and $\beta$ are roots of given equation. $(a \alpha+b)(a \beta+b)=a^{2} \alpha \beta+a b \alpha+a b \beta+b^{2}$
$=a^{2} \alpha \beta+a b(\alpha+\beta)+b^{2}$
From the given quadratic equation
$\alpha+\beta=\frac{-b}{a}, \alpha \beta=\frac{c}{a}$
$a^{2} \times \frac{c}{a}+a b \times-\frac{b}{a}+b^{2}=a c$
$=a^{2} \alpha \beta+a b(\alpha+\beta)+b^{2}$
From the given quadratic equation
$\alpha+\beta=\frac{-b}{a}, \alpha \beta=\frac{c}{a}$
$a^{2} \times \frac{c}{a}+a b \times-\frac{b}{a}+b^{2}=a c$
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