Question

If $\alpha$ and $\beta$are the roots of the equation $x^2+3x-4=0$,then$1/\alpha +1/\beta$is equal to

• A. $-3/4$
• B. $3/4$
• C. $-4/3$
• D. $4/3$
• E. $3/2$

Answer 1

The correct option is B

$3/4$

Find the value of $\mathbf{}\mathbf{1}\mathbf{/}\mathit{\alpha }\mathbf{}\mathbf{+}\mathbf{}\mathbf{1}\mathbf{/}\mathit{\beta }\mathbf{}$:

Given that $\alpha$ and $\beta$are the roots of the equation $x^2+3x-4=0$,

$\Rightarrow (\alpha +\beta )=-3$ and $\alpha .\beta =-4$

Now, $\frac{1}{\alpha }+\frac{1}{\beta }=\frac{(\beta +\alpha )}{\alpha \beta }$

$$\begin{gathered} \Rightarrow \frac{1}{\alpha }+\frac{1}{\beta }=\frac{-3}{-4} \\ \Rightarrow \frac{1}{\alpha }+\frac{1}{\beta }=\frac{3}{4} \end{gathered}$$

Hence, the correct option is B.