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

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

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

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

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

The solutions are

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

4 x^{4} + 8 x^{3} - 17 x^{2} - 21 x - 18 = 0

6 x^{4} - 45 x^{2} + 81 = 0

x^{8} + 16 = 17 x^{4}

y^{3} + 5 y^{2} - 36 y - 180 = 0

x^{4} + 49 x^{2} = 0

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