What are the solutions to the equation 2x^3-x+12=x^4 ?

The solutions to the equation 2x^3-x+12=x^4 are x\approx 2.56155…,x\approx-1.56155…

Find the zeros of 2x^3-x+12=x^4

The zeros of 2x^3-x+12=x^4 are x\approx 2.56155…,x\approx-1.56155…

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2 x^{3} - x + 12 = x^{4}

x \approx 2.56155 \dots, x \approx - 1.56155 \dots

Solution steps

2 x^{3} - x + 12 = x^{4}

Switch sides

x^{4} = 2 x^{3} - x + 12

Move

12

to the left side

x^{4} - 12 = 2 x^{3} - x

Move

x

to the left side

x^{4} - 12 + x = 2 x^{3}

Move

2 x^{3}

to the left side

x^{4} - 12 + x - 2 x^{3} = 0

Write in the standard form

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

x^{4} - 2 x^{3} + x - 12 = 0

Find one solution for

x^{4} - 2 x^{3} + x - 12 = 0

using Newton-Raphson:

x \approx 2.56155 \dots

Apply long division:

\frac{x ^{4} - 2 x ^{3} + x - 12}{x - 2.56155 \dots} = x^{3} + 0.56155 \dots x^{2} + 1.43844 \dots x + 4.68465 \dots

x^{3} + 0.56155 \dots x^{2} + 1.43844 \dots x + 4.68465 \dots \approx 0

Find one solution for

x^{3} + 0.56155 \dots x^{2} + 1.43844 \dots x + 4.68465 \dots = 0

using Newton-Raphson:

x \approx - 1.56155 \dots

Apply long division:

\frac{x ^{3} + 0.56155 \dots x ^{2} + 1.43844 \dots x + 4.68465 \dots}{x + 1.56155 \dots} = x^{2} - x + 3.00000 \dots

x^{2} - x + 3.00000 \dots \approx 0

Find one solution for

x^{2} - x + 3.00000 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 2.56155 \dots, x \approx - 1.56155 \dots

4 x^{3} - 12 x^{2} + 9 x = 0

0.16 = (1 + x)^{3} - 1

4 t^{3} + 6 t + 2.5 = 25

3 x^{2} \cdot 2 x = 162

x (x + 2) (x - 4) = 2

What are the solutions to the equation 2x^3-x+12=x^4 ?
The solutions to the equation 2x^3-x+12=x^4 are x\approx 2.56155…,x\approx-1.56155…
Find the zeros of 2x^3-x+12=x^4
The zeros of 2x^3-x+12=x^4 are x\approx 2.56155…,x\approx-1.56155…