Solve the following quadratic equations by factorization method: [2 MARKS]

$\sqrt{3} x^{2} + 10 x + 7 \sqrt{3} = 0$

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Solution

Concept : 1 Mark
Application : 1 Mark

$\sqrt{3} x^{2} + 10 x + 7 \sqrt{3} = 0$

$\Rightarrow \sqrt{3} x^{2} + 3 x + 7 x + 7 \sqrt{3} = 0$

$\Rightarrow \sqrt{3} x (x + \sqrt{3}) + 7 (x + \sqrt{3}) = 0$

$\Rightarrow (x + \sqrt{3}) (\sqrt{3} x + 7) = 0$

$\Rightarrow x + \sqrt{3} = 0, o r \sqrt{3} x + 7 = 0$

$\Rightarrow x = - \sqrt{3} o r x = - \frac{7}{\sqrt{3}}$

Thus, $x = - \sqrt{3}$ and $x = - \frac{7}{\sqrt{3}}$ are the two roots of the given equation.

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