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

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

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

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

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

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

The solutions are

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

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

n^{3} - 9 n^{2} - n + 9 = 0

y, 4 x^{3} - 16 y = 4 y^{3} - 16 x

4 x^{7} - 64 x^{3} = 0

N, b a^{2} + 3 = N^{3}

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