Question:
Solve the equation $x^{2}+3=0$
Solution:
Therefore, the required solutions are
The given quadratic equation is $x^{2}+3=0$
On comparing the given equation with $a x^{2}+b x+c=0$, we obtain
$a=1, b=0$, and $c=3$
Therefore, the discriminant of the given equation is
$D=b^{2}-4 a c=0^{2}-4 \times 1 \times 3=-12$
Therefore, the required solutions are
$\frac{-b \pm \sqrt{D}}{2 a}=\frac{\pm \sqrt{-12}}{2 \times 1}=\frac{\pm \sqrt{12} i}{2} \quad[\sqrt{-1}=i]$
$=\frac{\pm 2 \sqrt{3} i}{2}=\pm \sqrt{3} i$