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

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

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

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

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

r = 0, r = 1, r = 2, r = i, r = - i

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

r - 1 = 0 : r = 1

Solve

r - 2 = 0 : r = 2

Solve

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

The solutions are

r = 0, r = 1, r = 2, r = i, r = - i

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

x^{3} - 2 x^{2} - 11 x + 12

x^{4} + 9 x^{3} + 12 x^{2} - 34 x + 12 = 0

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

3 x^{3} - 81 = 0

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