Find the roots of the following quadratic equations by the factorisation method:
$ 3 x^{2}+5 \sqrt{5} x-10=0 $

Given:

Given quadratic equation is \( 3 x^{2}+5 \sqrt{5} x-10=0 \).

To do:

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

Solution:

\( 3 x^{2}+5 \sqrt{5} x-10=0 \)

$3 x^{2}+6 \sqrt{5} x-\sqrt{5} x-2 \sqrt{5}(\sqrt{5})=0$

$3 x(x+2 \sqrt{5})-\sqrt{5}(x+2 \sqrt{5})=0$

$(x+2 \sqrt{5})(3 x-\sqrt{5})=0$

$x+2 \sqrt{5}=0$ or $3 x-\sqrt{5} =0$

$x=-2 \sqrt{5}$ or $x=\frac{\sqrt{5}}{3}$

Hence, the roots of the given quadratic equation are $-2 \sqrt{5}, \frac{\sqrt{5}}{3}$.