What are the solutions to the equation 18x^4+6x^3-24x^2-8x=0 ?

The solutions to the equation 18x^4+6x^3-24x^2-8x=0 are x=0,x=-1/3 ,x=-2/(sqrt(3)),x= 2/(sqrt(3))

Find the zeros of 18x^4+6x^3-24x^2-8x=0

The zeros of 18x^4+6x^3-24x^2-8x=0 are x=0,x=-1/3 ,x=-2/(sqrt(3)),x= 2/(sqrt(3))

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18 x^{4} + 6 x^{3} - 24 x^{2} - 8 x = 0

x = 0, x = - \frac{1}{3}, x = - \frac{2}{3}, x = \frac{2}{3}

Decimal Notation

x = 0, x = - 0.33333 \dots, x = - 1.15470 \dots, x = 1.15470 \dots

Solution steps

18 x^{4} + 6 x^{3} - 24 x^{2} - 8 x = 0

Factor

18 x^{4} + 6 x^{3} - 24 x^{2} - 8 x : 2 x (3 x + 1) (3 x + 2) (3 x - 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x + 1 = 0 or 3 x + 2 = 0 or 3 x - 2 = 0

Solve

3 x + 1 = 0 : x = - \frac{1}{3}

Solve

3 x + 2 = 0 : x = - \frac{2}{3}

Solve

3 x - 2 = 0 : x = \frac{2}{3}

The solutions are

x = 0, x = - \frac{1}{3}, x = - \frac{2}{3}, x = \frac{2}{3}

x^{4} - 3 x^{3} - 3 x^{2} + 7 x + 6 = 0

x^{3} + 7 x^{2} - 3 x = 21

2 m^{3} (4 - 3 m) (5 m + \frac{2}{3}) = 0

5 x^{3} + 7 x^{2} - 20 x - 28 = 0

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

What are the solutions to the equation 18x^4+6x^3-24x^2-8x=0 ?
The solutions to the equation 18x^4+6x^3-24x^2-8x=0 are x=0,x=-1/3 ,x=-2/(sqrt(3)),x= 2/(sqrt(3))
Find the zeros of 18x^4+6x^3-24x^2-8x=0
The zeros of 18x^4+6x^3-24x^2-8x=0 are x=0,x=-1/3 ,x=-2/(sqrt(3)),x= 2/(sqrt(3))