# Solve the equation 2x2 + x + 1 = 0

Question:

Solve the equation $2 x^{2}+x+1=0$

Solution:

The given quadratic equation is $2 x^{2}+x+1=0$

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

$a=2, b=1$, and $c=1$

Therefore, the discriminant of the given equation is

$D=b^{2}-4 a c=1^{2}-4 \times 2 \times 1=1-8=-7$

Therefore, the required solutions are

$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-1 \pm \sqrt{-7}}{2 \times 2}=\frac{-1 \pm \sqrt{7} i}{4}$ $[\sqrt{-1}=i]$