Question

If the roots of the equation $2x^2+ax+b=0$ are reciprocals to each other, then the value of b is

• A. $-1$
• B. $-2$
• C. $2$
• D. $1$

Answer 1

The correct option is C $2$

$2x^2+ax+b=0$
Let one root $\alpha$ $\therefore$ other root $=\frac{1}{\alpha }$
Sum of the roots$=\alpha +\frac{1}{\alpha }=\frac{-a}{2}$
Product of the roots $=\alpha \times \frac{1}{\alpha }=\frac{b}{2}$
$\Rightarrow 1=\frac{b}{2}$
$\Rightarrow b=2$