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

The solutions to the equation x^4-3x^3+x+3=0 are x\approx 1.40169…,x\approx 2.71422…

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

The zeros of x^4-3x^3+x+3=0 are x\approx 1.40169…,x\approx 2.71422…

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

x \approx 1.40169 \dots, x \approx 2.71422 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 1.40169 \dots

Apply long division:

\frac{x ^{4} - 3 x ^{3} + x + 3}{x - 1.40169 \dots} = x^{3} - 1.59830 \dots x^{2} - 2.24033 \dots x - 2.14026 \dots

x^{3} - 1.59830 \dots x^{2} - 2.24033 \dots x - 2.14026 \dots \approx 0

Find one solution for

x^{3} - 1.59830 \dots x^{2} - 2.24033 \dots x - 2.14026 \dots = 0

using Newton-Raphson:

x \approx 2.71422 \dots

Apply long division:

\frac{x ^{3} - 1.59830 \dots x ^{2} - 2.24033 \dots x - 2.14026 \dots}{x - 2.71422 \dots} = x^{2} + 1.11592 \dots x + 0.78853 \dots

x^{2} + 1.11592 \dots x + 0.78853 \dots \approx 0

Find one solution for

x^{2} + 1.11592 \dots x + 0.78853 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.40169 \dots, x \approx 2.71422 \dots

x^{10} - 4 x^{4} - 100 x + 200 = 0

m^{3} + m^{2} - m - \frac{1}{2} = 0

(4 w + 3) (w + 4) (w - 2) (w + 6) = 0

- 2 x (x + 7) (x^{2} - 11) = 0

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

What are the solutions to the equation x^4-3x^3+x+3=0 ?
The solutions to the equation x^4-3x^3+x+3=0 are x\approx 1.40169…,x\approx 2.71422…
Find the zeros of x^4-3x^3+x+3=0
The zeros of x^4-3x^3+x+3=0 are x\approx 1.40169…,x\approx 2.71422…