Question

The roots of $\sqrt{2}{x}^2+8x+\sqrt{2}=0$ are

• A. equal
• B. non real
• C. reciprocals of each other
• D. equal and opposite in sign

Answer 1

The correct option is C reciprocals of each other

$\sqrt{2}{x}^2+8x+\sqrt{2}=0$
Since,
$D=64-4\times 2=56>0$
Roots are distinct and real.

Let $\alpha ,\beta$ be the roots.
As $a=c=\sqrt{2}$, so
$\alpha \beta =\frac{c}{a}=1\Rightarrow \alpha =\frac{1}{\beta }$
Roots are reciprocals.