What are the solutions to the equation z^4+2z^3-2z-1=0 ?

The solutions to the equation z^4+2z^3-2z-1=0 are z=-1,z=1

Find the zeros of z^4+2z^3-2z-1=0

The zeros of z^4+2z^3-2z-1=0 are z=-1,z=1

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z^{4} + 2 z^{3} - 2 z - 1 = 0

z = - 1, z = 1

Solution steps

z^{4} + 2 z^{3} - 2 z - 1 = 0

Factor

z^{4} + 2 z^{3} - 2 z - 1 : (z + 1)^{3} (z - 1)

(z + 1)^{3} (z - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

z + 1 = 0 or z - 1 = 0

Solve

z + 1 = 0 : z = - 1

Solve

z - 1 = 0 : z = 1

The solutions are

z = - 1, z = 1

4 x^{4} - 25 x^{2} + 36 = 0

x^{3} + 3 x^{2} + 4 x + 12 = 0

z^{8} - 16 i = 0

x^{4} - 2937 x^{2} + 100 = 0

x^{2} (x - 3) = 0

What are the solutions to the equation z^4+2z^3-2z-1=0 ?
The solutions to the equation z^4+2z^3-2z-1=0 are z=-1,z=1
Find the zeros of z^4+2z^3-2z-1=0
The zeros of z^4+2z^3-2z-1=0 are z=-1,z=1