Solve the equation x2 + 3 = 0

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

$\frac{-b \pm \sqrt{D}}{2 a}=\frac{\pm \sqrt{-12}}{2 \times 1}=\frac{\pm \sqrt{12} i}{2} \quad[\sqrt{-1}=i]$

$=\frac{\pm 2 \sqrt{3} i}{2}=\pm \sqrt{3} i$

 

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