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

Given:

Given quadratic equation is \( \frac{2}{5} x^{2}-x-\frac{3}{5}=0 \).

To do:

We have to find the roots of the given quadratic equation.

Solution:

\( \frac{2}{5} x^{2}-x-\frac{3}{5}=0 \)

Multiplying by 5 on both sides, we get,

$2x^2-5x-3=0$

$2 x^{2}-(6 x-x)-3=0$

$2 x^{2}-6 x+x-3 =0$

$2 x(x-3)+1(x-3) =0$

$(x-3)(2 x+1)=0$

$x-3=0$ or $2x+1=0$

$x=3$ or $x=-\frac{1}{2}$

Hence, the roots of the given quadratic equation are $-\frac{1}{2}, 3$. 

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Updated on: 10-Oct-2022

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