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

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

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

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

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5 x^{3} + x = 0

x = 0, x = \frac{1}{5} i, x = - \frac{1}{5} i

Solution steps

5 x^{3} + x = 0

Factor

5 x^{3} + x : x (5 x^{2} + 1)

x (5 x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 5 x^{2} + 1 = 0

Solve

5 x^{2} + 1 = 0 : x = \frac{1}{5} i, x = - \frac{1}{5} i

The solutions are

x = 0, x = \frac{1}{5} i, x = - \frac{1}{5} i

x^{3} - 10 x^{2} + 27 x - 18 = 0

x^{4} - 6 x^{3} + 13 x^{2} - 12 x = 0

(1 - x) (x + 2) 2 (x + 3) = 0

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

- λ^{3} + 6 λ^{2} - 11 λ + 6 = 0

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