Question

If $\alpha and\beta$ are the roots of $x^2+x-2=0$. Find the value of ${\alpha }^{-1}+{\beta }^{-1}$.

• A. 1
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. 3

Answer 1

The correct option is B $\frac{1}{2}$

Given equation is: $x^2+x-2=0$

$\alpha$ and $\beta$ are the roots of the given equation.

$\therefore \alpha +\beta =-1,\alpha \beta =-2$

${\alpha }^{-1}+{\beta }^{-1}=\frac{1}{\alpha }+\frac{1}{\beta }$

$=\frac{\beta +\alpha }{\alpha \beta }=\frac{-1}{-2}=\frac{1}{2}$