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

The solutions to the equation x^4-4x^3+4x^2+4x-5=0 are x=-1,x=1,x=2+i,x=2-i

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

The zeros of x^4-4x^3+4x^2+4x-5=0 are x=-1,x=1,x=2+i,x=2-i

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

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

Solution steps

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

Factor

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

(x + 1) (x - 1) (x^{2} - 4 x + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x - 1 = 0 or x^{2} - 4 x + 5 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

Solve

x^{2} - 4 x + 5 = 0 : x = 2 + i, x = 2 - i

The solutions are

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

y, x = 5 - (2 y)^{3}

6 x^{4} + x^{2} = 15

x^{2} (x + 3)^{2} = 176

2 x^{3} - 3 x^{2} + 5 x + 1 = 0

x, 9 x^{3} - 5 y^{2} = 7

What are the solutions to the equation x^4-4x^3+4x^2+4x-5=0 ?
The solutions to the equation x^4-4x^3+4x^2+4x-5=0 are x=-1,x=1,x=2+i,x=2-i
Find the zeros of x^4-4x^3+4x^2+4x-5=0
The zeros of x^4-4x^3+4x^2+4x-5=0 are x=-1,x=1,x=2+i,x=2-i