What are the solutions to the equation z^5-2z^4-z^3+6z-4=0 ?

The solutions to the equation z^5-2z^4-z^3+6z-4=0 are z=1,z=2,z=-1+i,z=-1-i

Find the zeros of z^5-2z^4-z^3+6z-4=0

The zeros of z^5-2z^4-z^3+6z-4=0 are z=1,z=2,z=-1+i,z=-1-i

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z^{5} - 2 z^{4} - z^{3} + 6 z - 4 = 0

z = 1, z = 2, z = - 1 + i, z = - 1 - i

Solution steps

z^{5} - 2 z^{4} - z^{3} + 6 z - 4 = 0

Factor

z^{5} - 2 z^{4} - z^{3} + 6 z - 4 : (z - 1)^{2} (z - 2) (z^{2} + 2 z + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

z - 1 = 0 or z - 2 = 0 or z^{2} + 2 z + 2 = 0

Solve

z - 1 = 0 : z = 1

Solve

z - 2 = 0 : z = 2

Solve

z^{2} + 2 z + 2 = 0 : z = - 1 + i, z = - 1 - i

The solutions are

z = 1, z = 2, z = - 1 + i, z = - 1 - i

\frac{64}{81} = 4 q^{3}

- b + 3 - 1 = 3 x^{4}

x^{5} - 2 = - x

\frac{16}{81} = r^{4}

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

What are the solutions to the equation z^5-2z^4-z^3+6z-4=0 ?
The solutions to the equation z^5-2z^4-z^3+6z-4=0 are z=1,z=2,z=-1+i,z=-1-i
Find the zeros of z^5-2z^4-z^3+6z-4=0
The zeros of z^5-2z^4-z^3+6z-4=0 are z=1,z=2,z=-1+i,z=-1-i