Question

What is the reciprocal sum of the roots for the equation $\frac{2}{3}{x}^2-\frac{1}{3}x=0$?

• A. $2$
• B. $\frac{1}{2}$
• C. $\frac{-1}{2}$
• D. $-2$

Answer 1

Answer: (A)

$2$

$\frac{2}{3}{x}^2-\frac{1}{3}x=0$
Take $\frac{1}{3}x$ common, we get
$\frac{1}{3}x(2x-1)=0$
$\frac{1}{3}x=0$, $2x-1=0$
$x=0,x=$ $\frac{1}{2}$ are the roots of the equation.
Reciprocal sum of the roots $=$ $\frac{1}{0+\frac{1}{2}}$ $=2$