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If $\alpha ,\beta \\$ are roots $ax^{2}+bx+c=0\\$ of then fin the value of $\frac{1}{\left ( a\alpha +b \right )}+\frac{1}{\left (a\beta +b \right )}$
Option: 1
$\frac{bc}{a}$

Option: 2
$\frac{ac}{b}$

Option: 3
$\frac{b}{ac}$

Option: 4
$\frac{a}{bc}$

Answers (1)

best_answer

As $\alpha$ is a root of

$ax^{2}+bx+c=0\\$

$\Rightarrow a\alpha ^{2}+b\alpha +c=0\\$

$\Rightarrow \alpha \left ( a\alpha +b \right )+c=0\\$

$\Rightarrow a\alpha +b=\frac{-c}{\alpha }\\$

Similarly $a\beta +b=\frac{-c}{\beta }\\$

$So,\frac{1}{a\alpha +b}+\frac{1}{a\beta +b}= \frac{\alpha }{-c}+\frac{\beta }{-c}\\$

$=\frac{-\left ( \alpha +\beta \right )}{c}=-\left ( \frac{-b}{a} \right )\frac{1}{c}\\$

$=\frac{b}{ac}$

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mansi

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