Question

Solve the equation $x^2+3x+5=0$ for $x$.

Answer 1

The given quadratic equation is $x^2+3x+5=0$

On comparing the given equation with ${ax}^2+bx+c=0$,
we obtain $a=1,b=3,$ and $c=5$

Therefore, the discriminant of the given equation is
$D=b^2-4ac=3^2-4\times 1\times 5=9-20=-11$

Therefore, the required solutions are

$x=\frac{-b\pm \sqrt{D}}{2a}=\frac{-3\pm \sqrt{-11}}{2\times 1}=\frac{-3\pm \sqrt{11}i}{2}$