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

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

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

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

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

The solutions are

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

3 x^{3} - 27 x = 0

2 y (y - 9) (y + 4) = 0

4 x^{3} - 12 x^{2} + 8 x = 0

x^{3} - 2 x^{2} = 4 x - 8

2 x^{4} - 15 x^{3} + 18 x^{2} = 0

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