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

The solutions to the equation x^4-2x^3-2x^2+3x-4=0 are x=-(sqrt(17)-1)/2 ,x=(sqrt(17)+1)/2

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

The zeros of x^4-2x^3-2x^2+3x-4=0 are x=-(sqrt(17)-1)/2 ,x=(sqrt(17)+1)/2

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

x = - \frac{17 - 1}{2}, x = \frac{17 + 1}{2}

Decimal Notation

x = - 1.56155 \dots, x = 2.56155 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx - 1.56155 \dots

Apply long division:

\frac{x ^{4} - 2 x ^{3} - 2 x ^{2} + 3 x - 4}{x + 1.56155 \dots} = x^{3} - 3.56155 \dots x^{2} + 3.56155 \dots x - 2.56155 \dots

x^{3} - 3.56155 \dots x^{2} + 3.56155 \dots x - 2.56155 \dots \approx 0

Find one solution for

x^{3} - 3.56155 \dots x^{2} + 3.56155 \dots x - 2.56155 \dots = 0

using Newton-Raphson:

x \approx 2.56155 \dots

Apply long division:

\frac{x ^{3} - 3.56155 \dots x ^{2} + 3.56155 \dots x - 2.56155 \dots}{x - 2.56155 \dots} = x^{2} - x + 1

x^{2} - x + 1 \approx 0

Find one solution for

x^{2} - x + 1 = 0

using Newton-Raphson:

No Solution for

x \in R

Approximate to algebraic form

x \approx - 1.56155 \dots : x = - \frac{17 - 1}{2}

x \approx 2.56155 \dots : x = \frac{17 + 1}{2}

x = - \frac{17 - 1}{2}, x = \frac{17 + 1}{2}

The solutions are

x = - \frac{17 - 1}{2}, x = \frac{17 + 1}{2}

x^{3} + x^{2} - 12 x = 0

x^{4} - 10 x^{2} + 25 = 0

x^{3} = 70

x^{6} + 9 x^{3} + 8 = 0

3 x^{4} - 12 x^{2} = 0

What are the solutions to the equation x^4-2x^3-2x^2+3x-4=0 ?
The solutions to the equation x^4-2x^3-2x^2+3x-4=0 are x=-(sqrt(17)-1)/2 ,x=(sqrt(17)+1)/2
Find the zeros of x^4-2x^3-2x^2+3x-4=0
The zeros of x^4-2x^3-2x^2+3x-4=0 are x=-(sqrt(17)-1)/2 ,x=(sqrt(17)+1)/2