Question

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

Answer 1

Given equation is $\frac{2}{5}{x}^2-x-\frac{3}{5}=0$
On multiplying by 5 on both sides, we get
$\Rightarrow 2x^2-5x-3=0$
$\Rightarrow 2x^2-(6x-x)-3=0$ [by splitting the middle term]
$\Rightarrow$ $2x^2$– 6x + x – 3 = 0
$\Rightarrow$ 2x (x – 3) + 1 (x – 3) = 0
Now, x – 3 = 0 $\Rightarrow$ x = 3
and 2x + 1 = 0 $\Rightarrow x=-\frac{1}{2}$
Hence, the roots of the equation $2x^2–5x–3=0$ are $-\frac{1}{2}$ and 3.