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

The solutions to the equation x^4-3x^3+8x-2=0 are x\approx 0.25573…,x\approx-1.45145…

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

The zeros of x^4-3x^3+8x-2=0 are x\approx 0.25573…,x\approx-1.45145…

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

x \approx 0.25573 \dots, x \approx - 1.45145 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.25573 \dots

Apply long division:

\frac{x ^{4} - 3 x ^{3} + 8 x - 2}{x - 0.25573 \dots} = x^{3} - 2.74426 \dots x^{2} - 0.70181 \dots x + 7.82052 \dots

x^{3} - 2.74426 \dots x^{2} - 0.70181 \dots x + 7.82052 \dots \approx 0

Find one solution for

x^{3} - 2.74426 \dots x^{2} - 0.70181 \dots x + 7.82052 \dots = 0

using Newton-Raphson:

x \approx - 1.45145 \dots

Apply long division:

\frac{x ^{3} - 2.74426 \dots x ^{2} - 0.70181 \dots x + 7.82052 \dots}{x + 1.45145 \dots} = x^{2} - 4.19571 \dots x + 5.38806 \dots

x^{2} - 4.19571 \dots x + 5.38806 \dots \approx 0

Find one solution for

x^{2} - 4.19571 \dots x + 5.38806 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.25573 \dots, x \approx - 1.45145 \dots

t = - t^{3} + 10 t^{2} - 29 t + 29

2 x^{3} + 3 x^{2} - 12 x + 6 = 0

x^{3} + 3 x^{2} + 2 x + 1 = 0

x^{3} - 12 x^{2} + 48 x - 63 = 0

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

What are the solutions to the equation x^4-3x^3+8x-2=0 ?
The solutions to the equation x^4-3x^3+8x-2=0 are x\approx 0.25573…,x\approx-1.45145…
Find the zeros of x^4-3x^3+8x-2=0
The zeros of x^4-3x^3+8x-2=0 are x\approx 0.25573…,x\approx-1.45145…