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

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

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

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

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

r = 0, r \approx - 0.77091 \dots

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

r = 0, r \approx - 0.77091 \dots

(5 x + 3)^{28} = \frac{16}{7}

- x^{3} + 27 x - 54 x = 0

(x - 2)^{6} + (x - 4)^{6} = 64

x, f (x)^{4} + f (- x)^{4} = x^{2000}

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

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