Question

If $\alpha$ and $\beta$ are roots of $a{x}^2+bx+c=0$, then $\frac{\beta }{a\alpha +b}+\frac{\alpha }{a\beta +b}$

• A. $-\frac{1}{a}$
• B. $-\frac{2}{a}$
• C. $-\frac{4}{a}$
• D. None of these

Answer 1

Answer: (B)

$-\frac{2}{a}$

Given $\alpha ,\beta$ are roots of $a{x}^2+bx+c=0$
$a{\alpha }^2+b\alpha +c=0\Rightarrow a\alpha +b=\frac{-c}{\alpha }$
$a{\beta }^2+b\beta +c=0\Rightarrow a\beta +b=\frac{-c}{\beta }$
$\frac{\beta }{a\alpha +b}+\frac{\alpha }{a\beta +b}=\frac{\alpha \beta }{-c}+\frac{\alpha \beta }{-c}=\frac{-2}{a}$
Hence, option B.