What are the solutions to the equation x^1-2x^2+3x^3=11 ?

The solutions to the equation x^1-2x^2+3x^3=11 are x\approx 1.71668…

Find the zeros of x^1-2x^2+3x^3=11

The zeros of x^1-2x^2+3x^3=11 are x\approx 1.71668…

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x^{1} - 2 x^{2} + 3 x^{3} = 11

x \approx 1.71668 \dots

Solution steps

x^{1} - 2 x^{2} + 3 x^{3} = 11

Refine

x - 2 x^{2} + 3 x^{3} = 11

Move

11

to the left side

x - 2 x^{2} + 3 x^{3} - 11 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

3 x^{3} - 2 x^{2} + x - 11 = 0

Find one solution for

3 x^{3} - 2 x^{2} + x - 11 = 0

using Newton-Raphson:

x \approx 1.71668 \dots

Apply long division:

\frac{3 x ^{3} - 2 x ^{2} + x - 11}{x - 1.71668 \dots} = 3 x^{2} + 3.15006 \dots x + 6.40768 \dots

3 x^{2} + 3.15006 \dots x + 6.40768 \dots \approx 0

Find one solution for

3 x^{2} + 3.15006 \dots x + 6.40768 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.71668 \dots

4 x^{3} + 4 = 0

x^{3} = \frac{4}{3}

y^{3} + (- 6) = - 9

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

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

What are the solutions to the equation x^1-2x^2+3x^3=11 ?
The solutions to the equation x^1-2x^2+3x^3=11 are x\approx 1.71668…
Find the zeros of x^1-2x^2+3x^3=11
The zeros of x^1-2x^2+3x^3=11 are x\approx 1.71668…