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# Find the Roots of the Quadratic Equation - Mathematics

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#### Question

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

#### Solution

We write, $7x = 5x + 2x as$ as $\sqrt{2} x^2 \times 5\sqrt{2} = 10 x^2 = 5x \times 2x$

$\therefore \sqrt{2} x^2 + 7x + 5\sqrt{2} = 0$

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

$\Rightarrow x\left( \sqrt{2}x + 5 \right) + \sqrt{2}\left( \sqrt{2}x + 5 \right) = 0$

$\Rightarrow \left( \sqrt{2}x + 5 \right)\left( x + \sqrt{2} \right) = 0$

$\Rightarrow x + \sqrt{2} = 0 \text { or } \sqrt{2}x + 5 = 0$

$\Rightarrow x = - \sqrt{2} \text { or } x = - \frac{5}{\sqrt{2}} = - \frac{5\sqrt{2}}{2}$Hence, the roots of the given equation are $- \sqrt{2} \text { and}$ $- \frac{5\sqrt{2}}{2}$.

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