Question

If $\alpha$ and $\beta$ are the zeroes of the polynomial $4x^2+3x+7$, then $\frac{1}{\alpha }+\frac{1}{\beta }$ is equal to:

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

Answer 1

The correct option is D $-\frac{3}{7}$

Given: $\alpha ,\beta$ are zeroes of the polynomial $4x^2+3x+7$

To find the value of $\frac{1}{\alpha }+\frac{1}{\beta }$

We know that equation $a{x}^2+bx+c=0$

Then sum of roots $=\frac{-b}{a}$ and product of roots$=\frac{c}{a}$

From the given quadratic equation,

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

Therefore,

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

$=\frac{-\frac{3}{4}}{\frac{7}{4}}=-\frac{3}{7}$

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