What are the solutions to the equation r^3-r^2+r-1=0 ?

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

Find the zeros of r^3-r^2+r-1=0

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

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r^{3} - r^{2} + r - 1 = 0

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

Solution steps

r^{3} - r^{2} + r - 1 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

r - 1 = 0 : r = 1

Solve

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

The solutions are

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

\frac{4 x ^{3} d - 1}{3} = 190

y, y = \frac{y ^{3}}{3}

x^{4} - 7 x + 12 = 0

18 x^{2} - 2.75 x^{3} = 3 (4 + 7 x)

x^{3} + 3 + 2 = 0

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