What are the solutions to the equation x^4+4x^3-3x^2-11x-6=0 ?

The solutions to the equation x^4+4x^3-3x^2-11x-6=0 are x\approx-4.16955…,x\approx 1.84037…

Find the zeros of x^4+4x^3-3x^2-11x-6=0

The zeros of x^4+4x^3-3x^2-11x-6=0 are x\approx-4.16955…,x\approx 1.84037…

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x^{4} + 4 x^{3} - 3 x^{2} - 11 x - 6 = 0

x \approx - 4.16955 \dots, x \approx 1.84037 \dots

Solution steps

x^{4} + 4 x^{3} - 3 x^{2} - 11 x - 6 = 0

Find one solution for

x^{4} + 4 x^{3} - 3 x^{2} - 11 x - 6 = 0

using Newton-Raphson:

x \approx - 4.16955 \dots

Apply long division:

\frac{x ^{4} + 4 x ^{3} - 3 x ^{2} - 11 x - 6}{x + 4.16955 \dots} = x^{3} - 0.16955 \dots x^{2} - 2.29305 \dots x - 1.43900 \dots

x^{3} - 0.16955 \dots x^{2} - 2.29305 \dots x - 1.43900 \dots \approx 0

Find one solution for

x^{3} - 0.16955 \dots x^{2} - 2.29305 \dots x - 1.43900 \dots = 0

using Newton-Raphson:

x \approx 1.84037 \dots

Apply long division:

\frac{x ^{3} - 0.16955 \dots x ^{2} - 2.29305 \dots x - 1.43900 \dots}{x - 1.84037 \dots} = x^{2} + 1.67082 \dots x + 0.78190 \dots

x^{2} + 1.67082 \dots x + 0.78190 \dots \approx 0

Find one solution for

x^{2} + 1.67082 \dots x + 0.78190 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 4.16955 \dots, x \approx 1.84037 \dots

x^{4} - x^{3} - 6 x^{2} = 0

Z^{4} = 16 i

- a^{3} + 5 a^{2} - 6 a = 0

- x^{5} + x = 0

6 x^{3} - 5 x^{2} - 7 x + 2 = 0

What are the solutions to the equation x^4+4x^3-3x^2-11x-6=0 ?
The solutions to the equation x^4+4x^3-3x^2-11x-6=0 are x\approx-4.16955…,x\approx 1.84037…
Find the zeros of x^4+4x^3-3x^2-11x-6=0
The zeros of x^4+4x^3-3x^2-11x-6=0 are x\approx-4.16955…,x\approx 1.84037…