Question

Find the roots of the following quadratic equation by factorisation method.
$2x^2+\frac{5}{3}x-2=0$

• A. $\frac{-3}{2}and\frac{2}{9}$
• B. $\frac{-3}{7}and\frac{2}{3}$
• C. $\frac{-3}{5}and\frac{2}{3}$
• D. $\frac{-3}{2}and\frac{2}{3}$

Answer 1

The correct option is D

$\frac{-3}{2}and\frac{2}{3}$

Given equation is $2x^2+\frac{5}{3}x-2=0$
On multiplying by 3 on both sides, we get
$6x^2+5x-6=0$
$\Rightarrow 6x^2+(9x-4x)-6=0$ [by splitting the middle term]
$\Rightarrow 6x^2+9x-4x-6=0\Rightarrow 3x(2x+3)-2(2x+3)=0\Rightarrow (2x+3)(3x-2)=0$
Now, $2x+3=0$
$\Rightarrow x=-\frac{3}{2}$
and $3x-2=0$
$\Rightarrow x=\frac{2}{3}$
Hence, the roots of the equation $6x^2+5x-6=0$ are $\frac{-3}{2}$ and $\frac{2}{3}$