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

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

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

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

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x^{5} - 3 x^{4} + 3 x^{3} - 3 x^{2} + 2 x = 0

x = 0, x = 1, x = 2, x = i, x = - i

Solution steps

x^{5} - 3 x^{4} + 3 x^{3} - 3 x^{2} + 2 x = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x - 2 = 0 : x = 2

Solve

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

The solutions are

x = 0, x = 1, x = 2, x = i, x = - i

x^{3} + 6 x^{2} - 32 = 0

10 + 8 y^{3} = 82

243 x^{5} + 32 = 100000

6 x^{4} - 5 x^{3} + 7 x^{2} - 5 x + 1 = 0

x^{3} + 5 x^{2} + 10 x + 50 = 0

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