Question

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$3x^2-2\sqrt{6}x+2=0$

Answer 1

Roots are given by $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{2\sqrt{6}\pm \sqrt{(-2\sqrt{6}{)}^2-4\times 2\times 3}}{2\times 3}$

$=\frac{2\sqrt{6}\pm 0}{6}$

$=\frac{\sqrt{6}}{3}$

We see that the roots are equal as the determinant is zero.