Question

Solve the equation : $x^2-2x+\frac{3}{2}=0$

Answer 1

This given equation can also be written as ${2x}^2-4x+3=0$
On comparing this equation with ${ax}^2+bx+c=0$,
we obtain $a=2,b=-4,$ and $c=3$
Therefore, the discriminant of the given equation is,
$D=b^2-4ac={(-4)}^2-4\times 2\times 3=16-24=-8$
Therefore, the required solutions are
$\frac{-b\pm \sqrt{D}}{2a}=\frac{-(-4)\pm \sqrt{-8}}{2\times 2}=\frac{4\pm 2\sqrt{2i}}{4}$
$=\frac{2\pm \sqrt{2}i}{2}=1\pm \frac{1}{\sqrt{2}}i$