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

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

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

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

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

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

Decimal Notation

x = 0, x = - 0.33333 \dots, x = - 0.70710 \dots, x = 0.70710 \dots

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

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

Solve

2 x - 1 = 0 : x = \frac{1}{2}

The solutions are

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

4 x^{3} - 256 = 0

2 x^{3} - 5 x^{2} + 4 x - 1 = 0

9 c^{3} + 12 c^{2} = 12 c^{2} + 36 c

x^{9} - x = 0

y^{4} + 2 y^{2} - 99 = 0

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