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

The solutions to the equation x^4-2x^2+8x-3=0 are x=sqrt(2)-1,x=-sqrt(2)-1

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

The zeros of x^4-2x^2+8x-3=0 are x=sqrt(2)-1,x=-sqrt(2)-1

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

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

Decimal Notation

x = 0.41421 \dots, x = - 2.41421 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.41421 \dots

Apply long division:

\frac{x ^{4} - 2 x ^{2} + 8 x - 3}{x - 0.41421 \dots} = x^{3} + 0.41421 \dots x^{2} - 1.82842 \dots x + 7.24264 \dots

x^{3} + 0.41421 \dots x^{2} - 1.82842 \dots x + 7.24264 \dots \approx 0

Find one solution for

x^{3} + 0.41421 \dots x^{2} - 1.82842 \dots x + 7.24264 \dots = 0

using Newton-Raphson:

x \approx - 2.41421 \dots

Apply long division:

\frac{x ^{3} + 0.41421 \dots x ^{2} - 1.82842 \dots x + 7.24264 \dots}{x + 2.41421 \dots} = x^{2} - 2 x + 3

x^{2} - 2 x + 3 \approx 0

Find one solution for

x^{2} - 2 x + 3 = 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

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

y^{3} = 18

y^{3} = 14

y^{3} = 11

2 x ((5) 4) = ((2) 5) x^{4}

What are the solutions to the equation x^4-2x^2+8x-3=0 ?
The solutions to the equation x^4-2x^2+8x-3=0 are x=sqrt(2)-1,x=-sqrt(2)-1
Find the zeros of x^4-2x^2+8x-3=0
The zeros of x^4-2x^2+8x-3=0 are x=sqrt(2)-1,x=-sqrt(2)-1