What are the solutions to the equation w^3-2w^2+w=2 ?

The solutions to the equation w^3-2w^2+w=2 are w=2,w=i,w=-i

Find the zeros of w^3-2w^2+w=2

The zeros of w^3-2w^2+w=2 are w=2,w=i,w=-i

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w^{3} - 2 w^{2} + w = 2

w = 2, w = i, w = - i

Solution steps

w^{3} - 2 w^{2} + w = 2

Move

2

to the left side

w^{3} - 2 w^{2} + w - 2 = 0

Factor

w^{3} - 2 w^{2} + w - 2 : (w - 2) (w^{2} + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

w - 2 = 0 : w = 2

Solve

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

The solutions are

w = 2, w = i, w = - i

x^{6} + 7 2^{3} + 512 = 0

k^{3} = 8

x^{4} + x^{3} + x^{2} + x^{1} = 1

(17 x - 11)^{3} - (17 x - 11) = 0

m^{3} = 1000

What are the solutions to the equation w^3-2w^2+w=2 ?
The solutions to the equation w^3-2w^2+w=2 are w=2,w=i,w=-i
Find the zeros of w^3-2w^2+w=2
The zeros of w^3-2w^2+w=2 are w=2,w=i,w=-i