What are the solutions to the equation x^4+3x+1=0 ?

The solutions to the equation x^4+3x+1=0 are x\approx-0.33766…,x\approx-1.30748…

Find the zeros of x^4+3x+1=0

The zeros of x^4+3x+1=0 are x\approx-0.33766…,x\approx-1.30748…

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x^{4} + 3 x + 1 = 0

x \approx - 0.33766 \dots, x \approx - 1.30748 \dots

Solution steps

x^{4} + 3 x + 1 = 0

Find one solution for

x^{4} + 3 x + 1 = 0

using Newton-Raphson:

x \approx - 0.33766 \dots

Apply long division:

\frac{x ^{4} + 3 x + 1}{x + 0.33766 \dots} = x^{3} - 0.33766 \dots x^{2} + 0.11401 \dots x + 2.96149 \dots

x^{3} - 0.33766 \dots x^{2} + 0.11401 \dots x + 2.96149 \dots \approx 0

Find one solution for

x^{3} - 0.33766 \dots x^{2} + 0.11401 \dots x + 2.96149 \dots = 0

using Newton-Raphson:

x \approx - 1.30748 \dots

Apply long division:

\frac{x ^{3} - 0.33766 \dots x ^{2} + 0.11401 \dots x + 2.96149 \dots}{x + 1.30748 \dots} = x^{2} - 1.64515 \dots x + 2.26503 \dots

x^{2} - 1.64515 \dots x + 2.26503 \dots \approx 0

Find one solution for

x^{2} - 1.64515 \dots x + 2.26503 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.33766 \dots, x \approx - 1.30748 \dots

x^{3} - 5 x + 6 = 2 \cdot 2

2 x^{3} + 3 x^{2} - 18 x - 27 = 0

81 x^{8} - 25 x^{4} = 0

x, x^{3} + 9 x = 0

0.5 g^{9} + 3.5 g = 11 - 0.5 g

What are the solutions to the equation x^4+3x+1=0 ?
The solutions to the equation x^4+3x+1=0 are x\approx-0.33766…,x\approx-1.30748…
Find the zeros of x^4+3x+1=0
The zeros of x^4+3x+1=0 are x\approx-0.33766…,x\approx-1.30748…