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

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

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

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

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

r = 0, r = - 1

Solution steps

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

Factor

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

r (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

x^{3} - 45 x = 4 x^{2}

- x^{4} + x^{2} - 4 x - 8 = 0

(3 - x) x^{2} = 0

0 = 3 x^{3} + 8 x^{2} - 15 x + 4

2 z^{4} + 32 = 0

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