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

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

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

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

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

x = 1, x = 5, x = i, x = - i

Solution steps

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

Factor

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

(x - 1) (x - 5) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x - 5 = 0 or x^{2} + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

x - 5 = 0 : x = 5

Solve

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

The solutions are

x = 1, x = 5, x = i, x = - i

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

z, (a) z^{4} = 24 i - 7

(x^{2} + 2 x - 3)^{2} = 0

2 x^{2} - 4 x^{4} = 5

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

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