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

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Solution

$\sqrt{2} x^{2} + 7 x + 5 \sqrt{2}$
$= \sqrt{2} x^{2} + 5 x + 2 x + 5 \sqrt{2}$ (Splitting the middle term 7x as 5x+2x because $5 x \times 2 x = 10 x^{2}$ )
$= x (\sqrt{2} x + 5) + \sqrt{2} (\sqrt{2} x + 5) = (\sqrt{2} x + 5) (x + \sqrt{2})$
Roots of this equation are the values for which $(\sqrt{2} x + 5) (x + \sqrt{2}) = 0$
$∴ \sqrt{2} x + 5 = 0 o r x + \sqrt{2} = 0$
$\Rightarrow x = - \frac{5}{\sqrt{2}} o r x = - \sqrt{2}$

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