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

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

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

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

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2 x^{3} - 4 x^{2} + 3 x = 1

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

Solution steps

2 x^{3} - 4 x^{2} + 3 x = 1

Move

1

to the left side

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

Factor

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

- 2 x (5 x - 8) (49 x^{2} - 9) = 0

16 x^{4} + 73 x^{2} + 36 = 0

i x^{6} - 1 = 0

w^{3} - 2 w^{2} + w = 2

x^{6} + 7 2^{3} + 512 = 0

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