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

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

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

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

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

r = 0, r = 1

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

r = 0 or r - 1 = 0

Solve

r - 1 = 0 : r = 1

The solutions are

r = 0, r = 1

r^{3} - 5 r^{2} + 3 r + 9 = 0

x^{5} - 10 x^{3} - 20 x^{2} - 15 x - 4 = 0

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

x^{4} + 11 x^{2} = 3 x^{2} + 128

y^{4} - 7 y^{2} = - 10

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