Solve each of the following quadratic equations:

Question:

Solve each of the following quadratic equations:

$x^{2}+3 \sqrt{3} x-30=0$

 

Solution:

We write, $3 \sqrt{3} x=5 \sqrt{3} x-2 \sqrt{3} x$ as $x^{2} \times(-30)=-30 x^{2}=5 \sqrt{3} x \times(-2 \sqrt{3} x)$

$\therefore x^{2}+3 \sqrt{3} x-30=0$

$\Rightarrow x^{2}+5 \sqrt{3} x-2 \sqrt{3} x-30=0$

$\Rightarrow x(x+5 \sqrt{3})-2 \sqrt{3}(x+5 \sqrt{3})=0$

$\Rightarrow(x+5 \sqrt{3})(x-2 \sqrt{3})=0$

$\Rightarrow x+5 \sqrt{3}=0$ or $x-2 \sqrt{3}=0$

$\Rightarrow x=-5 \sqrt{3}$ or $x=2 \sqrt{3}$

Hence, the roots of the given equation are $-5 \sqrt{3}$ and $2 \sqrt{3}$.

 

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