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

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

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

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

x - 2 = 0 : x = 2

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

x = x^{5} + 5 x^{3} + 3

9 a^{3} - 81 a = - 2 a^{2} + 18

x, 175 = 5 x^{3}

3 + 9 x^{8} - 6^{2} = A

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

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