Question

If the roots of the equation $a{x}^2-4x+a^2=0$ are imaginary and the sum of the roots is equal to their product, then $a$ is

• A. $-2$
• B. $4$
• C. $2$
• D. none of these

Answer 1

The correct option is C $2$

$a{x}^2-4x+a^2=0$
Sum of roots $=\frac{4}{a}$
Product of roots $=a$
Given, sum of roots $=$product of roots.
$\Rightarrow \frac{4}{a}=a$
$\Rightarrow a=2,-2$
But since, $D<0$, so $a>0$
Hence, $a=2$.