Solve the equation x2 + 3x + 9 = 0


Solve the equation $x^{2}+3 x+9=0$


The given quadratic equation is $x^{2}+3 x+9=0$

On comparing the given equation with $a x^{2}+b x+c=0$, we obtain

$a=1, b=3$, and $c=9$

Therefore, the discriminant of the given equation is

$D=b^{2}-4 a c=3^{2}-4 \times 1 \times 9=9-36=-27$

$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-3 \pm \sqrt{-27}}{2(1)}=\frac{-3 \pm 3 \sqrt{-3}}{2}=\frac{-3 \pm 3 \sqrt{3} i}{2}$ $[\sqrt{-1}=i]$

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