Question

Question 1 (vi)

Find the roots of the quadratic equations by using the quadratic formula in the following question.

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

Answer 1

Given equation is $x^2-3\sqrt{5}x+10=0$
on comparing with ax2 + bx c = 0 we have
a = 1, b = - 3$\sqrt{5}$ and c = 10
by quadratic formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$=\frac{-(-3\sqrt{5})\pm \sqrt{9\left(5\right)-4\left(1\right)(10}}{2\left(1\right)}$
$=\frac{3\sqrt{5}\pm \sqrt{45-40}}{2}=\frac{3\sqrt{5}\pm \sqrt{5}}{5}$
$=\frac{3\sqrt{5}+\sqrt{5}}{2},\frac{3\sqrt{5}-\sqrt{5}}{2}=2\sqrt{5},\sqrt{5}$
So, $2\sqrt{5}and\sqrt{5}$ are the roots of the given equation