What are the solutions to the equation x^4-6x^3+14x^2-14x+5=0 ?

The solutions to the equation x^4-6x^3+14x^2-14x+5=0 are x=1,x=2+i,x=2-i

Find the zeros of x^4-6x^3+14x^2-14x+5=0

The zeros of x^4-6x^3+14x^2-14x+5=0 are x=1,x=2+i,x=2-i

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x^{4} - 6 x^{3} + 14 x^{2} - 14 x + 5 = 0

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

Solution steps

x^{4} - 6 x^{3} + 14 x^{2} - 14 x + 5 = 0

Factor

x^{4} - 6 x^{3} + 14 x^{2} - 14 x + 5 : (x - 1)^{2} (x^{2} - 4 x + 5)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

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 = 2 + i, x = 2 - i

3 x^{5} - 20 x^{3} = 0

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

(X - 2) (X + 4) (X - 5) = 0

5 x^{4} = 80 x^{2}

- 3 x^{3} + 75 x = 0

What are the solutions to the equation x^4-6x^3+14x^2-14x+5=0 ?
The solutions to the equation x^4-6x^3+14x^2-14x+5=0 are x=1,x=2+i,x=2-i
Find the zeros of x^4-6x^3+14x^2-14x+5=0
The zeros of x^4-6x^3+14x^2-14x+5=0 are x=1,x=2+i,x=2-i