Question

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

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

Answer 1

The correct option is A

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

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]
$\Rightarrow 6x^2+9x-4x-6=0\Rightarrow 3x(2x+3)-2(2x+3)=0\Rightarrow (2x+3)(3x-2)=0Now,2x+3=0\Rightarrow x=-\frac{3}{2}and3x-2=0\Rightarrow x=\frac{2}{3}$
Hence, the roots of the equation $6x^2+5x-6=0are\frac{-3}{2}and\frac{2}{3}$