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

The solutions to the equation x^3-3x+4x-2=0 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

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

The zeros of x^3-3x+4x-2=0 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

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

x = 1, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

Solution steps

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

Refine

x^{3} + x - 2 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + x + 2 = 0 : x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

The solutions are

x = 1, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

\frac{( 5 x - 1 ) ^{3}}{2 ^{4}} = 4^{1}

- y + 4 y^{6} = - 3 y - 4 + y

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

x^{3} = 90

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

What are the solutions to the equation x^3-3x+4x-2=0 ?
The solutions to the equation x^3-3x+4x-2=0 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2
Find the zeros of x^3-3x+4x-2=0
The zeros of x^3-3x+4x-2=0 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2