Question

If $\alpha ,\beta$ are roots of the $4x^2+3x+7=0$, then the value of

$\frac{1}{\alpha }+\frac{1}{\beta }$is

• A. $\frac{4}{7}$
• B. $-\frac{3}{7}$
• C. $\frac{3}{7}$
• D. $-\frac{3}{4}$

Answer 1

Given equation:$4x^2+3x+7=0$

Also,$\alpha \&\beta$ are the roots of the equation.

Then, sum of the roots = $\alpha +\beta$

Product of the roots

$=\alpha \beta =\frac{Coeffecientterm}{Coeffecientof{x}^2}$=

$\frac{7}{4}$

$\therefore \frac{1}{\alpha }+\frac{1}{\beta }$= $\frac{\alpha +\beta }{\alpha \beta }$=$\frac{-\frac{3}{4}}{\frac{7}{4}}=-\frac{3}{4}$