Question

Solve: x² + x + 1 = 0.​

Answer 1

The answers are :

1. x = -1 + √3i
2. x = -1 - √3i

This problem can be solved using the quadratic equation.

x = -1 ± √1² - 4(1)(1) / 2a

x = -1 ± √1 - 4 / 2a

x = -1 ± √-3 / 2a

x = -1 ± i√3 / 2a (∴ i = √-1)

The possible values of x are :

• x = -1 + √3i
• x = -1 - √3i

Answer 2

`\sf x = (-1 + i√(3) )/(2) \quad or \quad (-1 - i√(3) )/(2)`

Step-by-step explanation:

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

Solve it using quadratic formula

`\sf x = ( -b \pm √(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 = (-1 \pm √(1^2 - 4(1)(1)) )/(2(1))`

`\sf \rightarrow x = (-1 \pm √(-3) )/(2)`

`\sf \rightarrow x = (-1 \pm i√(3) )/(2)`

`\sf \rightarrow x = (-1 + i√(3) )/(2) \quad or \quad (-1 - i√(3) )/(2)`