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

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

Find the zeros of r^4-r=0

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

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r^{4} - r = 0

r = 0, r = 1, r = - \frac{1}{2} + \frac{3}{2} i, r = - \frac{1}{2} - \frac{3}{2} i

Solution steps

r^{4} - r = 0

Factor

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

r (r^{3} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

r = 0 or r^{3} - 1 = 0

Solve

r^{3} - 1 = 0 : r = 1, r = - \frac{1}{2} + \frac{3}{2} i, r = - \frac{1}{2} - \frac{3}{2} i

The solutions are

r = 0, r = 1, r = - \frac{1}{2} + \frac{3}{2} i, r = - \frac{1}{2} - \frac{3}{2} i

y^{4} + 2 y^{3} + y^{2} + 8 y - 12 = 0

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

2 x^{3} x^{3} = 1 8^{2}

x^{3} - x^{2} - 36 x + 36 = 0

\frac{2}{3} x^{3} = 1

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