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4-1.Complex numbers
easy
Solve the equation $x^{2}+3=0$
A
$\pm \sqrt{3} i$
B
$\pm \sqrt{3} i$
C
$\pm \sqrt{3} i$
D
$\pm \sqrt{3} i$
Solution
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
$=\frac{-b \pm \sqrt{D}}{2 a}=\frac{\pm \sqrt{-12}}{2 \times 1}=\frac{\pm \sqrt{12} i}{2}$ $[\sqrt{1}=i]$
$=\frac{\pm 2 \sqrt{3} i}{2}=\pm \sqrt{3} i$
Standard 11
Mathematics
