What are the solutions to the equation 27x^5+8x^2=0 ?

The solutions to the equation 27x^5+8x^2=0 are x=0,x=-2/3 ,x= 1/3-1/(sqrt(3))i,x= 1/3+1/(sqrt(3))i

Find the zeros of 27x^5+8x^2=0

The zeros of 27x^5+8x^2=0 are x=0,x=-2/3 ,x= 1/3-1/(sqrt(3))i,x= 1/3+1/(sqrt(3))i

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27 x^{5} + 8 x^{2} = 0

x = 0, x = - \frac{2}{3}, x = \frac{1}{3} - \frac{1}{3} i, x = \frac{1}{3} + \frac{1}{3} i

Solution steps

27 x^{5} + 8 x^{2} = 0

Factor

27 x^{5} + 8 x^{2} : x^{2} (27 x^{3} + 8)

x^{2} (27 x^{3} + 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 27 x^{3} + 8 = 0

Solve

27 x^{3} + 8 = 0 : x = - \frac{2}{3}, x = \frac{1}{3} - \frac{1}{3} i, x = \frac{1}{3} + \frac{1}{3} i

The solutions are

x = 0, x = - \frac{2}{3}, x = \frac{1}{3} - \frac{1}{3} i, x = \frac{1}{3} + \frac{1}{3} i

49 - x^{5} = 17

x (x + 5) = (x^{2} + 5 x)^{2}

4 = (1 + \frac{r}{2})^{20}

9 x^{3} - 4 = 0

X^{3} - 64 X = 0

What are the solutions to the equation 27x^5+8x^2=0 ?
The solutions to the equation 27x^5+8x^2=0 are x=0,x=-2/3 ,x= 1/3-1/(sqrt(3))i,x= 1/3+1/(sqrt(3))i
Find the zeros of 27x^5+8x^2=0
The zeros of 27x^5+8x^2=0 are x=0,x=-2/3 ,x= 1/3-1/(sqrt(3))i,x= 1/3+1/(sqrt(3))i