What are the solutions to the equation x^4-4x^3+8x^2-16x+16=0 ?

The solutions to the equation x^4-4x^3+8x^2-16x+16=0 are x=2,x=2i,x=-2i

Find the zeros of x^4-4x^3+8x^2-16x+16=0

The zeros of x^4-4x^3+8x^2-16x+16=0 are x=2,x=2i,x=-2i

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x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16 = 0

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

Solution steps

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16 = 0

Factor

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16 : (x - 2)^{2} (x^{2} + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

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

The solutions are

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

w^{3} = 512

3 x^{4} - 2 x^{3} + 2 x^{2} - 8 x - 40 = 0

x, x^{1000} + y^{1000} = 5

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

x^{6} - x^{3} - 2 = 0

What are the solutions to the equation x^4-4x^3+8x^2-16x+16=0 ?
The solutions to the equation x^4-4x^3+8x^2-16x+16=0 are x=2,x=2i,x=-2i
Find the zeros of x^4-4x^3+8x^2-16x+16=0
The zeros of x^4-4x^3+8x^2-16x+16=0 are x=2,x=2i,x=-2i