Solve the equation x2 + 3x + 5 = 0
Question:

Solve the equation $x^{2}+3 x+5=0$

Solution:

The given quadratic equation is $x^{2}+3 x+5=0$

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

$a=1, b=3$, and $c=5$

Therefore, the discriminant of the given equation is

$\mathrm{D}=b^{2}-4 a c=3^{2}-4 \times 1 \times 5=9-20=-11$

Therefore, the required solutions are

$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-3 \pm \sqrt{-11}}{2 \times 1}=\frac{-3 \pm \sqrt{11} i}{2}$ $[\sqrt{-1}=i]$

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