What are the solutions to the equation x^4-3x^3+6x^2-12x+8=0 ?

The solutions to the equation x^4-3x^3+6x^2-12x+8=0 are x=1,x=2,x=2i,x=-2i

Find the zeros of x^4-3x^3+6x^2-12x+8=0

The zeros of x^4-3x^3+6x^2-12x+8=0 are x=1,x=2,x=2i,x=-2i

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x^{4} - 3 x^{3} + 6 x^{2} - 12 x + 8 = 0

x = 1, x = 2, x = 2 i, x = - 2 i

Solution steps

x^{4} - 3 x^{3} + 6 x^{2} - 12 x + 8 = 0

Factor

x^{4} - 3 x^{3} + 6 x^{2} - 12 x + 8 : (x - 1) (x - 2) (x^{2} + 4)

(x - 1) (x - 2) (x^{2} + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 4 = 0 : x = 2 i, x = - 2 i

The solutions are

x = 1, x = 2, x = 2 i, x = - 2 i

x^{5} - 2 x^{4} - 24 x^{3} = 0

x^{3} - 2 x - 2 = 1.5

2 x^{3} + 3 x^{2} + 8 x + 12 = 0

x^{3} - 8 x^{2} + 12 x - 4 = 0

c^{3} = 46

What are the solutions to the equation x^4-3x^3+6x^2-12x+8=0 ?
The solutions to the equation x^4-3x^3+6x^2-12x+8=0 are x=1,x=2,x=2i,x=-2i
Find the zeros of x^4-3x^3+6x^2-12x+8=0
The zeros of x^4-3x^3+6x^2-12x+8=0 are x=1,x=2,x=2i,x=-2i