What are the solutions to the equation 0= 1/6 x^3-x ?

The solutions to the equation 0= 1/6 x^3-x are x=0,x=-sqrt(6),x=sqrt(6)

Find the zeros of 0= 1/6 x^3-x

The zeros of 0= 1/6 x^3-x are x=0,x=-sqrt(6),x=sqrt(6)

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0 = \frac{1}{6} x^{3} - x

x = 0, x = - 6, x = 6

Decimal Notation

x = 0, x = - 2.44948 \dots, x = 2.44948 \dots

Solution steps

0 = \frac{1}{6} x^{3} - x

Switch sides

\frac{1}{6} x^{3} - x = 0

Factor

\frac{1}{6} x^{3} - x : x (\frac{1}{6} x + 1) (\frac{1}{6} x - 1)

x (\frac{1}{6} x + 1) (\frac{1}{6} x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or \frac{1}{6} x + 1 = 0 or \frac{1}{6} x - 1 = 0

Solve

\frac{1}{6} x + 1 = 0 : x = - 6

Solve

\frac{1}{6} x - 1 = 0 : x = 6

The solutions are

x = 0, x = - 6, x = 6

x^{4} + 2 x^{3} - 3 x^{2} + 10 x + 25 = 0

12 x^{4} - 12 x^{3} + 1 = 0

4 x + 4 = (5 - 4 x)^{3}

x^{3} - x^{2} - 5 x + 21 = 0

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

What are the solutions to the equation 0= 1/6 x^3-x ?
The solutions to the equation 0= 1/6 x^3-x are x=0,x=-sqrt(6),x=sqrt(6)
Find the zeros of 0= 1/6 x^3-x
The zeros of 0= 1/6 x^3-x are x=0,x=-sqrt(6),x=sqrt(6)