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

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

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

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

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

r = - 1, r = 1, r = 1 + i, r = 1 - i

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

r + 1 = 0 : r = - 1

Solve

r - 1 = 0 : r = 1

Solve

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

The solutions are

r = - 1, r = 1, r = 1 + i, r = 1 - i

3 x^{3} - 81 = 0

6 y^{2} + 2 y - 5 y^{4} = 0

x^{3} - 594 x + 3186 = 0

2 x^{3} + 6 x = 0

x^{4} - 6 x^{3} - 3 x^{2} + 24 x - 4 = 0

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