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

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

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

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

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

The solutions are

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

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

16 x^{4} = 81

x^{4} + x^{3} + 7 x^{2} + 9 x - 18 = 0

x^{9} - 1 = 0

2 a^{3} - 3 a^{2} + 1 = 0

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