What are the solutions to the equation 0=3x^8+11x^5+4x+6 ?

The solutions to the equation 0=3x^8+11x^5+4x+6 are x\approx-0.78566…,x\approx-1.54293…

Find the zeros of 0=3x^8+11x^5+4x+6

The zeros of 0=3x^8+11x^5+4x+6 are x\approx-0.78566…,x\approx-1.54293…

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0 = 3 x^{8} + 11 x^{5} + 4 x + 6

x \approx - 0.78566 \dots, x \approx - 1.54293 \dots

Solution steps

0 = 3 x^{8} + 11 x^{5} + 4 x + 6

Switch sides

3 x^{8} + 11 x^{5} + 4 x + 6 = 0

Find one solution for

3 x^{8} + 11 x^{5} + 4 x + 6 = 0

using Newton-Raphson:

x \approx - 0.78566 \dots

Apply long division:

\frac{3 x ^{8} + 11 x ^{5} + 4 x + 6}{x + 0.78566 \dots} = 3 x^{7} - 2.35698 \dots x^{6} + 1.85180 \dots x^{5} + 9.54510 \dots x^{4} - 7.49924 \dots x^{3} + 5.89187 \dots x^{2} - 4.62903 \dots x + 7.63685 \dots

3 x^{7} - 2.35698 \dots x^{6} + 1.85180 \dots x^{5} + 9.54510 \dots x^{4} - 7.49924 \dots x^{3} + 5.89187 \dots x^{2} - 4.62903 \dots x + 7.63685 \dots \approx 0

Find one solution for

3 x^{7} - 2.35698 \dots x^{6} + 1.85180 \dots x^{5} + 9.54510 \dots x^{4} - 7.49924 \dots x^{3} + 5.89187 \dots x^{2} - 4.62903 \dots x + 7.63685 \dots = 0

using Newton-Raphson:

x \approx - 1.54293 \dots

Apply long division:

\frac{3 x ^{7} - 2.35698 \dots x ^{6} + 1.85180 \dots x ^{5} + 9.54510 \dots x ^{4} - 7.49924 \dots x ^{3} + 5.89187 \dots x ^{2} - 4.62903 \dots x + 7.63685 \dots}{x + 1.54293 \dots} = 3 x^{6} - 6.98580 \dots x^{5} + 12.63047 \dots x^{4} - 9.94293 \dots x^{3} + 7.84210 \dots x^{2} - 6.20801 \dots x + 4.94955 \dots

3 x^{6} - 6.98580 \dots x^{5} + 12.63047 \dots x^{4} - 9.94293 \dots x^{3} + 7.84210 \dots x^{2} - 6.20801 \dots x + 4.94955 \dots \approx 0

Find one solution for

3 x^{6} - 6.98580 \dots x^{5} + 12.63047 \dots x^{4} - 9.94293 \dots x^{3} + 7.84210 \dots x^{2} - 6.20801 \dots x + 4.94955 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.78566 \dots, x \approx - 1.54293 \dots

x^{3} - 300 x = 3000

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

x^{3} - x + 6 = 0

98 x - 49 = 2 x^{3} - x^{2}

x^{4} = - 256

What are the solutions to the equation 0=3x^8+11x^5+4x+6 ?
The solutions to the equation 0=3x^8+11x^5+4x+6 are x\approx-0.78566…,x\approx-1.54293…
Find the zeros of 0=3x^8+11x^5+4x+6
The zeros of 0=3x^8+11x^5+4x+6 are x\approx-0.78566…,x\approx-1.54293…