What are the solutions to the equation z^3+2z^2+21z-58=0 ?

The solutions to the equation z^3+2z^2+21z-58=0 are z=2,z=-2+5i,z=-2-5i

Find the zeros of z^3+2z^2+21z-58=0

The zeros of z^3+2z^2+21z-58=0 are z=2,z=-2+5i,z=-2-5i

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z^{3} + 2 z^{2} + 21 z - 58 = 0

z = 2, z = - 2 + 5 i, z = - 2 - 5 i

Solution steps

z^{3} + 2 z^{2} + 21 z - 58 = 0

Factor

z^{3} + 2 z^{2} + 21 z - 58 : (z - 2) (z^{2} + 4 z + 29)

(z - 2) (z^{2} + 4 z + 29) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

z - 2 = 0 or z^{2} + 4 z + 29 = 0

Solve

z - 2 = 0 : z = 2

Solve

z^{2} + 4 z + 29 = 0 : z = - 2 + 5 i, z = - 2 - 5 i

The solutions are

z = 2, z = - 2 + 5 i, z = - 2 - 5 i

x^{3} + 4 x^{2} - 36 x - 144 = 0

x^{3} - 9 x^{2} - 4 = 0

2 x^{3} - 5 x^{2} - 3 x = 0

6 x^{4} - 7 x^{2} + 2 = 0

x^{3} + 2 x^{2} + x - 1 = 0

What are the solutions to the equation z^3+2z^2+21z-58=0 ?
The solutions to the equation z^3+2z^2+21z-58=0 are z=2,z=-2+5i,z=-2-5i
Find the zeros of z^3+2z^2+21z-58=0
The zeros of z^3+2z^2+21z-58=0 are z=2,z=-2+5i,z=-2-5i