Question

Sum of the reciprocals of the roots of the equation $x^2+px+q=0$ is

• A. $-\frac{1}{p}$
• B. $\frac{p}{q}$
• C. $-\frac{p}{q}$
• D. $-\frac{1}{q}$

Answer 1

The correct option is C $-\frac{p}{q}$

Let the two roots be $\alpha$ and $\beta$. Then
Sum of the roots $\Rightarrow \alpha +\beta =-p$ ...(1) $[\because -\frac{b}{a}=-p]$

Product of the roots $\Rightarrow \alpha \beta =q$ ...(2)

Now, sum of the reciprocals of the roots will be $\frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }=-\frac{p}{q}$