What are the solutions to the equation 6x^4-x^3+5x^2-x-1=0 ?

The solutions to the equation 6x^4-x^3+5x^2-x-1=0 are x= 1/2 ,x=-1/3 ,x=i,x=-i

Find the zeros of 6x^4-x^3+5x^2-x-1=0

The zeros of 6x^4-x^3+5x^2-x-1=0 are x= 1/2 ,x=-1/3 ,x=i,x=-i

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

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

Solution steps

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

Factor

6 x^{4} - x^{3} + 5 x^{2} - x - 1 : (2 x - 1) (3 x + 1) (x^{2} + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

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

Solve

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

The solutions are

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

y, x = y^{3} + 1

2 x^{4} - 3 x^{2} - 20 = 0

x^{8} - 8 = 0

x^{4} - 3 x^{2} = - 2

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

What are the solutions to the equation 6x^4-x^3+5x^2-x-1=0 ?
The solutions to the equation 6x^4-x^3+5x^2-x-1=0 are x= 1/2 ,x=-1/3 ,x=i,x=-i
Find the zeros of 6x^4-x^3+5x^2-x-1=0
The zeros of 6x^4-x^3+5x^2-x-1=0 are x= 1/2 ,x=-1/3 ,x=i,x=-i