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

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

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

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

r - 1 = 0 : r = 1

Solve

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

The solutions are

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

x^{4} + 3 x^{3} + 3 x^{2} + 3 x + 2 = 0

5 x^{3} = 405 x

x^{4} - x^{3} - 4 x^{2} - x - 3 = 0

x^{3} - 9 x^{2} + 27 x - 27

r^{3} - 2 r^{2} - 5 r + 6 = 0

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