Solve

$x^{2} + 3 x + 9 = 0$

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Solution

Here $x^{2} + 3 x + 9 = 0$

Comparing the given quadratic equation with

$a x^{2} + b x + c = 0$ we have

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

$∴ x = \frac{- 3 \pm \sqrt{(3)^{2} - 4 \times 1 \times 9}}{2 \times 1}$

$= \frac{- 3 \pm \sqrt{- 27}}{2} = \frac{- 3 \pm 3 \sqrt{3} i}{2}$

Thus $x = \frac{- 3 + 3 \sqrt{3} i}{2}$ and $x = \frac{- 3 - 3 \sqrt{3} i}{2}$

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