Solve b^4 - b^2 - 2b -1

Evaluate

b^{4} - b^{2} - 2 b - 1

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

b^{4} - b^{2} - 2 b - 1 = 0

Factor the expression

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

b = \frac{1 + 5}{2} b = \frac{1 - 5}{2} b^{2} + b + 1 = 0

Solve the equation

More Steps

b = \frac{1 + 5}{2} b = \frac{1 - 5}{2} b = - \frac{1}{2} + \frac{3}{2} i b = - \frac{1}{2} - \frac{3}{2} i

Solution

b_{1} = - \frac{1}{2} - \frac{3}{2} i, b_{2} = - \frac{1}{2} + \frac{3}{2} i, b_{3} = \frac{1 - 5}{2}, b_{4} = \frac{1 + 5}{2}

Alternative Form

b_{1} \approx - 0.5 - 0.866025 i, b_{2} \approx - 0.5 + 0.866025 i, b_{3} \approx - 0.618034, b_{4} \approx 1.618034

Factor the expression