Solve each of the following quadratic equations:

Question:

Solve each of the following quadratic equations:

$x^{2}-3 \sqrt{5} x+10=0$

 

Solution:

We write, $-3 \sqrt{5} x=-2 \sqrt{5} x-\sqrt{5} x$ as $x^{2} \times 10=10 x^{2}=(-2 \sqrt{5} x) \times(-\sqrt{5} x)$

$\therefore x^{2}-3 \sqrt{5} x+10=0$

$\Rightarrow x^{2}-2 \sqrt{5} x-\sqrt{5} x+10=0$

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

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

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

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

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

 

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