Question

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

Answer 1

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 $\frac{2}{3}$