What are the solutions to the equation x^5+125x^2=0 ?

The solutions to the equation x^5+125x^2=0 are x=0,x=-5,x= 5/2-(5sqrt(3))/2 i,x= 5/2+(5sqrt(3))/2 i

Find the zeros of x^5+125x^2=0

The zeros of x^5+125x^2=0 are x=0,x=-5,x= 5/2-(5sqrt(3))/2 i,x= 5/2+(5sqrt(3))/2 i

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x^{5} + 125 x^{2} = 0

x = 0, x = - 5, x = \frac{5}{2} - \frac{5 3}{2} i, x = \frac{5}{2} + \frac{5 3}{2} i

Solution steps

x^{5} + 125 x^{2} = 0

Factor

x^{5} + 125 x^{2} : x^{2} (x^{3} + 125)

x^{2} (x^{3} + 125) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} + 125 = 0

Solve

x^{3} + 125 = 0 : x = - 5, x = \frac{5}{2} - \frac{5 3}{2} i, x = \frac{5}{2} + \frac{5 3}{2} i

The solutions are

x = 0, x = - 5, x = \frac{5}{2} - \frac{5 3}{2} i, x = \frac{5}{2} + \frac{5 3}{2} i

0 = 4 x^{4} - 17 x^{2} + 4

6 x^{3} = 11 x^{2} + 10 x

x^{4} - 6 x^{3} + 9 x^{2} = 0

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

4 x^{3} + 5 x^{2} + 36 x + 45 = 0

What are the solutions to the equation x^5+125x^2=0 ?
The solutions to the equation x^5+125x^2=0 are x=0,x=-5,x= 5/2-(5sqrt(3))/2 i,x= 5/2+(5sqrt(3))/2 i
Find the zeros of x^5+125x^2=0
The zeros of x^5+125x^2=0 are x=0,x=-5,x= 5/2-(5sqrt(3))/2 i,x= 5/2+(5sqrt(3))/2 i