Question

If the quadratic equation $a{x}^2+bx+c=0$ has two non-zero roots $\alpha \&\beta ,$, then find the valaue of $\frac{1}{\alpha }+\frac{1}{\beta }.$

• A. $-\frac{b}{c}$
• B. $bc$
• C. $-\frac{bc}{a^2}$
• D. $\frac{b}{c}$

Answer 1

The correct option is A $-\frac{b}{c}$

Since, $\alpha \&\beta$ are the two non-zero roots of $a{x}^2+bx+c=0.$
$\Rightarrow \alpha +\beta =-\frac{b}{a}\&\alpha \cdot \beta =\frac{c}{a}$

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