Question

If $\alpha$ and $\beta$ are the roots of $a{x}^2+bx+c=0,$ find the value of $\frac{1}{a\alpha +b}+\frac{1}{a\beta +b}$ .

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

Answer 1

Answer: (A)

$\frac{b}{ac}$

Given, $\alpha$ and $\beta$ are roots of the $a{x}^2+bx+c=0,$

$\frac{1}{a\alpha +b}+\frac{1}{a\beta +a}$

Put the value of $\alpha ,\beta$ in given quadratic and find values then put in Denominator.

$=-\frac{\alpha }{c}-\frac{\beta }{c}$

$=-\frac{1}{c}(\alpha +\beta )$

$=-\frac{1}{c}(-\frac{b}{a})$

$=\frac{b}{ac}$