Question

Solve: x² + x + 1 = 0.​

Answer 1

Answer:

$\sf x = \dfrac{-1 + i\sqrt{3} }{2} \quad or \quad \dfrac{-1 - i\sqrt{3} }{2}$

Explanation:

$\sf Given : x^2 + x + 1 = 0$

Solve it using quadratic formula

$\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad \:when\: \: ax^2 + bx + c = 0$

So, here constants are: a = 1, b = 1, c = 1

When the value's are substituted inside the formula

$\sf \rightarrow x = \dfrac{-1 \pm \sqrt{1^2 - 4(1)(1)} }{2(1)}$

$\sf \rightarrow x = \dfrac{-1 \pm \sqrt{-3} }{2}$

$\sf \rightarrow x = \dfrac{-1 \pm i\sqrt{3} }{2}$

$\sf \rightarrow x = \dfrac{-1 + i\sqrt{3} }{2} \quad or \quad \dfrac{-1 - i\sqrt{3} }{2}$