What are the solutions to the equation x^4-4x^3+5x^2-4x+4=0 ?

The solutions to the equation x^4-4x^3+5x^2-4x+4=0 are x=2,x=i,x=-i

Find the zeros of x^4-4x^3+5x^2-4x+4=0

The zeros of x^4-4x^3+5x^2-4x+4=0 are x=2,x=i,x=-i

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

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

Solution steps

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

Factor

x^{4} - 4 x^{3} + 5 x^{2} - 4 x + 4 : (x - 2)^{2} (x^{2} + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

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

The solutions are

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

(x - 5) (x^{2} + 4 x + 4) = 8 (x + 2)

3 x^{3} - 19 x^{2} + 33 x - 9 = 0

6 x^{3} + 25 x^{2} - 24 x + 5

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

x^{3} + 5 x + 5 = 0

What are the solutions to the equation x^4-4x^3+5x^2-4x+4=0 ?
The solutions to the equation x^4-4x^3+5x^2-4x+4=0 are x=2,x=i,x=-i
Find the zeros of x^4-4x^3+5x^2-4x+4=0
The zeros of x^4-4x^3+5x^2-4x+4=0 are x=2,x=i,x=-i