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

The solutions to the equation x^4+3x^3-2=0 are x\approx 0.80689…,x\approx-3.06917…

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

The zeros of x^4+3x^3-2=0 are x\approx 0.80689…,x\approx-3.06917…

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

x \approx 0.80689 \dots, x \approx - 3.06917 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.80689 \dots

Apply long division:

\frac{x ^{4} + 3 x ^{3} - 2}{x - 0.80689 \dots} = x^{3} + 3.80689 \dots x^{2} + 3.07178 \dots x + 2.47862 \dots

x^{3} + 3.80689 \dots x^{2} + 3.07178 \dots x + 2.47862 \dots \approx 0

Find one solution for

x^{3} + 3.80689 \dots x^{2} + 3.07178 \dots x + 2.47862 \dots = 0

using Newton-Raphson:

x \approx - 3.06917 \dots

Apply long division:

\frac{x ^{3} + 3.80689 \dots x ^{2} + 3.07178 \dots x + 2.47862 \dots}{x + 3.06917 \dots} = x^{2} + 0.73772 \dots x + 0.80758 \dots

x^{2} + 0.73772 \dots x + 0.80758 \dots \approx 0

Find one solution for

x^{2} + 0.73772 \dots x + 0.80758 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.80689 \dots, x \approx - 3.06917 \dots

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

6 x^{5} + 10 x^{3} + 2 = 0

2.5 x^{3} + 1.56 x^{2} - 3 x + 1.5 = 0

- x^{3} - 6 x^{2} - 9 x + 4 = 0

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

What are the solutions to the equation x^4+3x^3-2=0 ?
The solutions to the equation x^4+3x^3-2=0 are x\approx 0.80689…,x\approx-3.06917…
Find the zeros of x^4+3x^3-2=0
The zeros of x^4+3x^3-2=0 are x\approx 0.80689…,x\approx-3.06917…