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

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

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

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

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3 x^{3} + x = 0

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

Solution steps

3 x^{3} + x = 0

Factor

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

x (3 x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x^{2} + 1 = 0

Solve

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

The solutions are

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

2 (x + 6) (16 x^{2} - 25) = 0

x^{2} (x - 2) - 4 (x - 2) = 0

(1 + x)^{3} = 1.3

x^{6} - 3 x^{2} - 2 = 0

3 x^{3} + 20 x^{2} - 7 x = 0

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