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

The solutions to the equation roots x^4-4x^3+5x^2-2x-2 are x=-sqrt(2)+1,x=sqrt(2)+1

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

The zeros of roots x^4-4x^3+5x^2-2x-2 are x=-sqrt(2)+1,x=sqrt(2)+1

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roots

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

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

Solution steps

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

The roots are the intercepts with the x-axis

(y = 0)

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.41421 \dots

Apply long division:

\frac{x ^{4} - 4 x ^{3} + 5 x ^{2} - 2 x - 2}{x + 0.41421 \dots} = x^{3} - 4.41421 \dots x^{2} + 6.82842 \dots x - 4.82842 \dots

x^{3} - 4.41421 \dots x^{2} + 6.82842 \dots x - 4.82842 \dots \approx 0

Find one solution for

x^{3} - 4.41421 \dots x^{2} + 6.82842 \dots x - 4.82842 \dots = 0

using Newton-Raphson:

x \approx 2.41421 \dots

Apply long division:

\frac{x ^{3} - 4.41421 \dots x ^{2} + 6.82842 \dots x - 4.82842 \dots}{x - 2.41421 \dots} = x^{2} - 2 x + 2

x^{2} - 2 x + 2 \approx 0

Find one solution for

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

using Newton-Raphson:

No Solution for

x \in R

Approximate to algebraic form

x \approx - 0.41421 \dots : x = - 2 + 1

x \approx 2.41421 \dots : x = 2 + 1

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

The solutions are

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

x^{3} - 9 x^{2} + 21 x - 5 = 0

200 x - 0.02 x^{2} - 0.000002 x^{3} - 80000 = 0

(1 + 12 x^{2})^{3} = 0

2 x^{3} - 14 x^{2} + 2 x - 14 = 0

24 x^{3} + 46 x^{2} + 9 x - 9 = 0

What are the solutions to the equation roots x^4-4x^3+5x^2-2x-2 ?
The solutions to the equation roots x^4-4x^3+5x^2-2x-2 are x=-sqrt(2)+1,x=sqrt(2)+1
Find the zeros of roots x^4-4x^3+5x^2-2x-2
The zeros of roots x^4-4x^3+5x^2-2x-2 are x=-sqrt(2)+1,x=sqrt(2)+1