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

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

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

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

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

x = 1, x = i, x = - i

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

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

The solutions are

x = 1, x = i, x = - i

81 x^{4} - 16 = 0

x^{3} - 8 x^{2} + 17 x - 10 = 0

x^{4} + 6 x^{3} - 33 x^{2} - 46 x + 72 = 0

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

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

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