Question

If quadratic equation $6x^2-7x+2=0$ has one root $\frac{1}{2}$ then the second root will be--

• A. $-\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{3}{2}$
• D. 1

Answer 1

The correct option is B $\frac{2}{3}$

Let the second root of the quadratic equation $6x^2-7x+2=0$ be $\alpha$

Then as per question--
$\because$ Sum of the roots = $\alpha +\frac{1}{2}=\frac{7}{6}$
$\Rightarrow$ $\alpha =\frac{7}{6}-\frac{1}{2}=\frac{7-3}{6}=\frac{2}{3}$
$\Rightarrow$ Product of the roots = $\alpha \times \frac{1}{2}=\frac{2}{6}$
$\Rightarrow$ $\alpha =\frac{1}{3}\times 2=\frac{2}{3}$
$\therefore$ Second root = $\frac{2}{3}$