What are the solutions to the equation (p)=p^3+1 ?

The solutions to the equation (p)=p^3+1 are p\approx-1.32471…

Find the zeros of (p)=p^3+1

The zeros of (p)=p^3+1 are p\approx-1.32471…

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(p) = p^{3} + 1

p \approx - 1.32471 \dots

Solution steps

(p) = p^{3} + 1

Refine

p = p^{3} + 1

Switch sides

p^{3} + 1 = p

Move

p

to the left side

p^{3} + 1 - p = 0

Write in the standard form

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

p^{3} - p + 1 = 0

Find one solution for

p^{3} - p + 1 = 0

using Newton-Raphson:

p \approx - 1.32471 \dots

Apply long division:

\frac{p ^{3} - p + 1}{p + 1.32471 \dots} = p^{2} - 1.32471 \dots p + 0.75487 \dots

p^{2} - 1.32471 \dots p + 0.75487 \dots \approx 0

Find one solution for

p^{2} - 1.32471 \dots p + 0.75487 \dots = 0

using Newton-Raphson:

No Solution for

p \in R

The solution is

p \approx - 1.32471 \dots

t^{4} - t^{2} - 2 = 0

x, 171 y = 3 x^{5}

(x^{2} - 4) (x - 2) = 0

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

n^{3} - n - 6 = 0

What are the solutions to the equation (p)=p^3+1 ?
The solutions to the equation (p)=p^3+1 are p\approx-1.32471…
Find the zeros of (p)=p^3+1
The zeros of (p)=p^3+1 are p\approx-1.32471…