Find the roots of the following quadratic equations by factorization:
$\sqrt{2} x^{2} + 7 x + 5 \sqrt{2} = 0$

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Solution

By factorising,

$\sqrt{2} x^{2} + 5 x + 2 x + 5 \sqrt{2} = 0$

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

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

=> $x = - \sqrt{5}$ and $x = \frac{- 5}{\sqrt{2}}$

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