Find the zeroes of the polynomial $5 x^{2} - 2$ .

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Solution

Let $f (x) = 5 x^{2} - 2$
Using formula $a^{2} - b^{2} = (a + b) (a - b)$
$(\sqrt{5} x - \sqrt{2}) (\sqrt{5} x + \sqrt{2})$
$f (x) = 0$ ,when $\sqrt{5} x - \sqrt{2} = 0$ or $\sqrt{5} x + \sqrt{2} = 0$
when $x = \sqrt{\frac{2}{5}}$ or $x = - \frac{\sqrt{2}}{\sqrt{5}}$
Hence the zeroes of the polynomial $5 x^{2} - 2$ are $\frac{\sqrt{2}}{\sqrt{5}}, - \frac{\sqrt{2}}{\sqrt{5}}$

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