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

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

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

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

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

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

Solution steps

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

Factor

x^{4} - 2 x^{3} + x - 2 : (x - 2) (x + 1) (x^{2} - x + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x + 1 = 0 : x = - 1

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

(2 x + 1) (2 x + 3) (2 x + 5) (2 x + 7) = 9

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

x, 0 = x^{4} - 8 x^{2} - 9

43 = a^{3}

x^{8} + 4 x^{2} + 4 = 0

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