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

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

Find the zeros of roots 2x^3-x^2+2x-1

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

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roots

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

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

Solution steps

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

The roots are the intercepts with the x-axis

(y = 0)

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

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

The solutions are

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

6 x^{3} + 36 x - 12 = 0

x^{4} = x^{5}

(2 x + 1)^{3} = 900

11 x^{10} - 60 x^{9} = 0

- x^{3} + 0.8 x^{2} + 0.260625 x - 0.08775 = 0

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