Solve x^4 +x^2 +1

Question

Factor the expression

(x^{2} - x + 1) (x^{2} + x + 1)

Show Solution

x_{1} = - \frac{1}{2} - \frac{3}{2} i, x_{2} = - \frac{1}{2} + \frac{3}{2} i, x_{3} = \frac{1}{2} - \frac{3}{2} i, x_{4} = \frac{1}{2} + \frac{3}{2} i

Alternative Form

x_{1} \approx - 0.5 - 0.866025 i, x_{2} \approx - 0.5 + 0.866025 i, x_{3} \approx 0.5 - 0.866025 i, x_{4} \approx 0.5 + 0.866025 i

Evaluate

x^{4} + x^{2} + 1

To find the roots of the expression,set the expression equal to 0

x^{4} + x^{2} + 1 = 0

Factor the expression

(x^{2} - x + 1) (x^{2} + x + 1) = 0

Separate the equation into 2 possible cases

x^{2} - x + 1 = 0 x^{2} + x + 1 = 0

Solve the equation

More Steps

x = \frac{1}{2} + \frac{3}{2} i x = \frac{1}{2} - \frac{3}{2} i x^{2} + x + 1 = 0

Solve the equation

More Steps

x = \frac{1}{2} + \frac{3}{2} i x = \frac{1}{2} - \frac{3}{2} i x = - \frac{1}{2} + \frac{3}{2} i x = - \frac{1}{2} - \frac{3}{2} i

Solution

x_{1} = - \frac{1}{2} - \frac{3}{2} i, x_{2} = - \frac{1}{2} + \frac{3}{2} i, x_{3} = \frac{1}{2} - \frac{3}{2} i, x_{4} = \frac{1}{2} + \frac{3}{2} i

Alternative Form

x_{1} \approx - 0.5 - 0.866025 i, x_{2} \approx - 0.5 + 0.866025 i, x_{3} \approx 0.5 - 0.866025 i, x_{4} \approx 0.5 + 0.866025 i

Show Solution