Find the roots of the following quadratic equation:

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

The given quadratic equation is ${\mathrm{x}}^2-3\sqrt[ ]{5}\mathrm{x}+10=0$. 

On comparing with the standard form of quadratic equation i.e., ax² + bx + c = 0, we obtain 

a = 1,  b = -$-3\sqrt{5}$ , c = 10

$\begin{array}{c}\sqrt{\mathrm{D}}=\sqrt{{\mathrm{b}}^2-4\mathrm{ac}}=\sqrt{5}\\ \Rightarrow \mathrm{x}=\frac{-\mathrm{b}\pm \sqrt{\mathrm{D}}}{2\mathrm{a}}=\frac{3\sqrt{5}\pm \sqrt{5}}{2}=2\sqrt{5},\sqrt{5}\end{array}$

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