Question

If $\alpha ,\beta$ are the roots of the equation $a{x}^2+bx+c=0$ then the value of $\{\frac{1}{aa+b}+\frac{1}{a\beta +b}\}$ is

• A. $\frac{a}{bc}$
• B. $\frac{b}{ac}$
• C. $\frac{c}{ab}$
• D. None

Answer 1

Answer: (B)

$\frac{b}{ac}$

Since $\alpha ,\beta$ are the roots of the given equation

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

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

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

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