Question

Solve for $x:$ $3x^2-\sqrt{6}x+2=0.$

Answer 1

The given quadratic equation is $3x^2-\sqrt{6}x+2=0$

Comparing with the quadratic equation $a{x}^2+bx+c=0$, we have

$a=3,b=-\sqrt{6},c=2$

Discriminant of the given quadratic equation,

$D=b^2-4ac\Rightarrow (-\sqrt{6}{)}^2-4(3\left)\right(2)=\sqrt{-18}$

Therefore, $x=\frac{-b\pm \sqrt{D}}{2a}$

$x=\frac{-(-\sqrt{6})\pm \sqrt{-18}}{6}$

$x=\frac{1}{\sqrt{6}}\pm \frac{\sqrt{-2}}{2}.$