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

The solutions to the equation roots 2+3x^2-x^3 are x\approx 3.19582…

Find the zeros of roots 2+3x^2-x^3

The zeros of roots 2+3x^2-x^3 are x\approx 3.19582…

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roots

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

x \approx 3.19582 \dots

Solution steps

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

The roots are the intercepts with the x-axis

(y = 0)

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx 3.19582 \dots

Apply long division:

\frac{- x ^{3} + 3 x ^{2} + 2}{x - 3.19582 \dots} = - x^{2} - 0.19582 \dots x - 0.62581 \dots

- x^{2} - 0.19582 \dots x - 0.62581 \dots \approx 0

Find one solution for

- x^{2} - 0.19582 \dots x - 0.62581 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 3.19582 \dots

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

x^{6} - 64

x (x + 6) (x + 2) = 64

52 x^{3} - 29 x - 1 = 0

x^{3} - 4 x = 5 x^{2} - 20

What are the solutions to the equation roots 2+3x^2-x^3 ?
The solutions to the equation roots 2+3x^2-x^3 are x\approx 3.19582…
Find the zeros of roots 2+3x^2-x^3
The zeros of roots 2+3x^2-x^3 are x\approx 3.19582…