Question

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

Answer 1

Here $x^2-2x+\frac{3}{2}=0$

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

$a=1,b=-2and=\frac{3}{2}$

$\therefore x=\frac{-(-2)\pm \sqrt{(-2{)}^2-4\times 1\times \frac{3}{2}}}{2\times 1}$

$=\frac{2\pm \sqrt{4-6}}{2}=\frac{2\pm \sqrt{-2}}{2}$

$=\frac{2\pm \sqrt{2}i}{2}=1\pm \frac{\sqrt{2}}{2}i$

Thus $x=1+\frac{\sqrt{2}}{2}i$

and $x=1-\frac{\sqrt{2}}{2}i$