Question

The roots of the equation $2a^2{x}^2-2abx+b^2=0$ when a < 0 and b > 0 are :

• A. Sometimes complex
• B. Always irrational
• C. Always complex
• D. Always real

Answer 1

The correct option is C Always complex

For an equation $a{x}^2+bx+c=0$, where $a\ne 0$ to have real roots, D must be greater than or equal to 0, where

$D=b^2-4ac$

In the given equation, $2a^2{x}^2-2abx+b^2=0$

$D=(-2ab{)}^2-4\times (2a^2)\times (b^2)$

$\Rightarrow D=-6a^2{b}^2$

$\because a,b\ne 0\Rightarrow -6a^2{b}^2$ is always negative

We see that $D$ is strictly negative

Hence, the equation always has complex roots.