What are the solutions to the equation x=-3x^4+2x^3-5x+8 ?

The solutions to the equation x=-3x^4+2x^3-5x+8 are x\approx 1.07701…,x\approx-1.38386…

Find the zeros of x=-3x^4+2x^3-5x+8

The zeros of x=-3x^4+2x^3-5x+8 are x\approx 1.07701…,x\approx-1.38386…

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x = - 3 x^{4} + 2 x^{3} - 5 x + 8

x \approx 1.07701 \dots, x \approx - 1.38386 \dots

Solution steps

x = - 3 x^{4} + 2 x^{3} - 5 x + 8

Switch sides

- 3 x^{4} + 2 x^{3} - 5 x + 8 = x

Move

x

to the left side

- 3 x^{4} + 2 x^{3} - 6 x + 8 = 0

Find one solution for

- 3 x^{4} + 2 x^{3} - 6 x + 8 = 0

using Newton-Raphson:

x \approx 1.07701 \dots

Apply long division:

\frac{- 3 x ^{4} + 2 x ^{3} - 6 x + 8}{x - 1.07701 \dots} = - 3 x^{3} - 1.23103 \dots x^{2} - 1.32584 \dots x - 7.42795 \dots

- 3 x^{3} - 1.23103 \dots x^{2} - 1.32584 \dots x - 7.42795 \dots \approx 0

Find one solution for

- 3 x^{3} - 1.23103 \dots x^{2} - 1.32584 \dots x - 7.42795 \dots = 0

using Newton-Raphson:

x \approx - 1.38386 \dots

Apply long division:

\frac{- 3 x ^{3} - 1.23103 \dots x ^{2} - 1.32584 \dots x - 7.42795 \dots}{x + 1.38386 \dots} = - 3 x^{2} + 2.92056 \dots x - 5.36752 \dots

- 3 x^{2} + 2.92056 \dots x - 5.36752 \dots \approx 0

Find one solution for

- 3 x^{2} + 2.92056 \dots x - 5.36752 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.07701 \dots, x \approx - 1.38386 \dots

x^{3} - 2 x^{2} + 1 = 0

(x + 1)^{3} = (2 x)^{3}

x, x^{3} + y^{3} = 8

2000 x^{3} = 1000

x = 33 x^{2} + 4 x^{3} - 10 x^{2}

What are the solutions to the equation x=-3x^4+2x^3-5x+8 ?
The solutions to the equation x=-3x^4+2x^3-5x+8 are x\approx 1.07701…,x\approx-1.38386…
Find the zeros of x=-3x^4+2x^3-5x+8
The zeros of x=-3x^4+2x^3-5x+8 are x\approx 1.07701…,x\approx-1.38386…