Browse Questions

# Solve $\;x^{2} + x + 1=0$

$(a)\;\large\frac{\pm \sqrt{3}i}{2}\qquad(b)\;\large\frac{1+ \sqrt{3}i}{2}\qquad(c)\;\large\frac{-1\pm \sqrt{3}i}{5}\qquad(d)\;\large\frac{-1\pm \sqrt{3}i}{2}$

Answer : $\;\large\frac{-1\pm \sqrt{3}i}{2}$
Explanation :
we have , $\;x^{2} + x + 1=0$
$b^{2} - 4ac = 1^{2} - 4 \times 1 \times 1$
$=1-4 = 3$
Therefore , the solutions are given by
$x= \large\frac{-1 \pm \sqrt{-3}}{2 \times 1}$
$x= \large\frac{-1 \pm \sqrt{3}i}{2}$