Question

If $\alpha ,\beta ϵR$ and the quadratic equations $x^2+2x+7=0$ and $4x^2+\alpha x+\beta =0$ have atleast one common roots, then the value of $\alpha +\beta$ is:-

• A. $-4$
• B. $36$
• C. $20$
• D. $24$

Answer 1

The correct option is B $36$

The quadratic equations are

$x^2+2x+7=0$ & $4x^2+2x+\beta =0$

For first equation $D=b^2-4ac$

$=2^2-4\left(1\right)\left(7\right)=-27<0$

$\Rightarrow$ Both roots are imaginary, which means one root can't be common.

$\Rightarrow$ Both roots are common.

$\Rightarrow \frac{4}{1}=\frac{\alpha }{2}=\frac{\beta }{7}$

$\Rightarrow \alpha =8$ and $\beta =28$

$\alpha +\beta =8+28=36$