What are the solutions to the equation 3x^5+x-7=0 ?

The solutions to the equation 3x^5+x-7=0 are x\approx 1.14316…

Find the zeros of 3x^5+x-7=0

The zeros of 3x^5+x-7=0 are x\approx 1.14316…

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3 x^{5} + x - 7 = 0

x \approx 1.14316 \dots

Solution steps

3 x^{5} + x - 7 = 0

Find one solution for

3 x^{5} + x - 7 = 0

using Newton-Raphson:

x \approx 1.14316 \dots

Apply long division:

\frac{3 x ^{5} + x - 7}{x - 1.14316 \dots} = 3 x^{4} + 3.42949 \dots x^{3} + 3.92046 \dots x^{2} + 4.48173 \dots x + 6.12335 \dots

3 x^{4} + 3.42949 \dots x^{3} + 3.92046 \dots x^{2} + 4.48173 \dots x + 6.12335 \dots \approx 0

Find one solution for

3 x^{4} + 3.42949 \dots x^{3} + 3.92046 \dots x^{2} + 4.48173 \dots x + 6.12335 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.14316 \dots

(x + 3) (x^{2} + 2 x + 6) = - (x + 3) (x - 4)

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

2 x^{2} - 8 x^{3} = 8

x^{4} + 16 x^{2} = 0

x^{4} - 10 x^{2} - 9 = 0

What are the solutions to the equation 3x^5+x-7=0 ?
The solutions to the equation 3x^5+x-7=0 are x\approx 1.14316…
Find the zeros of 3x^5+x-7=0
The zeros of 3x^5+x-7=0 are x\approx 1.14316…