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

The solutions to the equation 2x^3+x^2-1=1 are x\approx 0.85809…

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

The zeros of 2x^3+x^2-1=1 are x\approx 0.85809…

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

x \approx 0.85809 \dots

Solution steps

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

Move

1

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.85809 \dots

Apply long division:

\frac{2 x ^{3} + x ^{2} - 2}{x - 0.85809 \dots} = 2 x^{2} + 2.71618 \dots x + 2.33074 \dots

2 x^{2} + 2.71618 \dots x + 2.33074 \dots \approx 0

Find one solution for

2 x^{2} + 2.71618 \dots x + 2.33074 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.85809 \dots

x^{3} - 3 x^{2} - 9 x + 5 = 0

x^{2} (x + 1) = 252

(x - 2) (x + 9) (x - 1) = 0

(x - 5) (x^{2} + x + 1) = 0

x^{3} + 11 x^{2} + 23 x - 35 = 0

What are the solutions to the equation 2x^3+x^2-1=1 ?
The solutions to the equation 2x^3+x^2-1=1 are x\approx 0.85809…
Find the zeros of 2x^3+x^2-1=1
The zeros of 2x^3+x^2-1=1 are x\approx 0.85809…