What are the solutions to the equation x^5+2x^3+2x^2=0 ?

The solutions to the equation x^5+2x^3+2x^2=0 are x=0,x\approx-0.77091…

Find the zeros of x^5+2x^3+2x^2=0

The zeros of x^5+2x^3+2x^2=0 are x=0,x\approx-0.77091…

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x^{5} + 2 x^{3} + 2 x^{2} = 0

x = 0, x \approx - 0.77091 \dots

Solution steps

x^{5} + 2 x^{3} + 2 x^{2} = 0

Factor

x^{5} + 2 x^{3} + 2 x^{2} : x^{2} (x^{3} + 2 x + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x^{3} + 2 x + 2 = 0 : x \approx - 0.77091 \dots

The solutions are

x = 0, x \approx - 0.77091 \dots

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

m^{3} - m^{2} + 8 m - 8 = 0

z^{4} = 82 + 82 i

0 = x^{3} - 5 x^{2} - x + 5

x^{3} - 7 x^{2} + 4 x + 30 = 0

What are the solutions to the equation x^5+2x^3+2x^2=0 ?
The solutions to the equation x^5+2x^3+2x^2=0 are x=0,x\approx-0.77091…
Find the zeros of x^5+2x^3+2x^2=0
The zeros of x^5+2x^3+2x^2=0 are x=0,x\approx-0.77091…