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

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

Find the zeros of 2x^3+x=0

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

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2 x^{3} + x = 0

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

Solution steps

2 x^{3} + x = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

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

x^{4} - 6 x^{2} - 27 = 0

x^{4} + 2 x + 1 = 0

(2 x - 15)^{5} = (2 x - 15)^{3}

\frac{x ^{4} + 9}{10} = x^{2}

y^{6} - 10 y^{3} + 16 = 0

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