What are the solutions to the equation 3x^3-19^2+36x-10=0 ?

The solutions to the equation 3x^3-19^2+36x-10=0 are x\approx 4.18731…

Find the zeros of 3x^3-19^2+36x-10=0

The zeros of 3x^3-19^2+36x-10=0 are x\approx 4.18731…

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3 x^{3} - 1 9^{2} + 36 x - 10 = 0

x \approx 4.18731 \dots

Solution steps

3 x^{3} - 1 9^{2} + 36 x - 10 = 0

Expand

3 x^{3} - 1 9^{2} + 36 x - 10 : 3 x^{3} + 36 x - 371

3 x^{3} + 36 x - 371 = 0

Find one solution for

3 x^{3} + 36 x - 371 = 0

using Newton-Raphson:

x \approx 4.18731 \dots

Apply long division:

\frac{3 x ^{3} + 36 x - 371}{x - 4.18731 \dots} = 3 x^{2} + 12.56195 \dots x + 88.60087 \dots

3 x^{2} + 12.56195 \dots x + 88.60087 \dots \approx 0

Find one solution for

3 x^{2} + 12.56195 \dots x + 88.60087 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 4.18731 \dots

4 x^{4} = 256 x

(3 x + 7) (x^{2} - 100) = 0

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

y^{3} + y^{2} = 36 y + 36

1031 = x^{5} + x + 3

What are the solutions to the equation 3x^3-19^2+36x-10=0 ?
The solutions to the equation 3x^3-19^2+36x-10=0 are x\approx 4.18731…
Find the zeros of 3x^3-19^2+36x-10=0
The zeros of 3x^3-19^2+36x-10=0 are x\approx 4.18731…