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

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Solution

Given equation is $3 x^{2} + 5 \sqrt{5}$ x – 10 = 0
$3 x^{2} + 6 \sqrt{5} x - \sqrt{5} x - 10 = 0$
$3 x^{2} + 6 \sqrt{5} x - \sqrt{5 x} - \sqrt{5} x - 10 = 0$
$\Rightarrow 3 x (x + 2 \sqrt{5}) - \sqrt{5} (x + 2 \sqrt{5}) = 0$
$\Rightarrow (x + 2 \sqrt{5}) (3 x - \sqrt{5}) = 0$
Now, x + 2 $\sqrt{5}$ = 0
$\Rightarrow x = - 2 \sqrt{5} a n d 3 x - \sqrt{5} = 0$
$\Rightarrow x = \frac{\sqrt{5}}{3}$
Hence, the roots of the equation $3 x^{2} + 5 \sqrt{5} x - 10 = 0 a r e - 2 \sqrt{5} a n d \frac{\sqrt{5}}{3}$

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