What are the solutions to the equation 3018=x^4-x^3-7x^2+9x ?

The solutions to the equation 3018=x^4-x^3-7x^2+9x are x\approx 7.88916…,x\approx-7.43798…

Find the zeros of 3018=x^4-x^3-7x^2+9x

The zeros of 3018=x^4-x^3-7x^2+9x are x\approx 7.88916…,x\approx-7.43798…

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3018 = x^{4} - x^{3} - 7 x^{2} + 9 x

x \approx 7.88916 \dots, x \approx - 7.43798 \dots

Solution steps

3018 = x^{4} - x^{3} - 7 x^{2} + 9 x

Switch sides

x^{4} - x^{3} - 7 x^{2} + 9 x = 3018

Move

3018

to the left side

x^{4} - x^{3} - 7 x^{2} + 9 x - 3018 = 0

Find one solution for

x^{4} - x^{3} - 7 x^{2} + 9 x - 3018 = 0

using Newton-Raphson:

x \approx 7.88916 \dots

Apply long division:

\frac{x ^{4} - x ^{3} - 7 x ^{2} + 9 x - 3018}{x - 7.88916 \dots} = x^{3} + 6.88916 \dots x^{2} + 47.34975 \dots x + 382.55000 \dots

x^{3} + 6.88916 \dots x^{2} + 47.34975 \dots x + 382.55000 \dots \approx 0

Find one solution for

x^{3} + 6.88916 \dots x^{2} + 47.34975 \dots x + 382.55000 \dots = 0

using Newton-Raphson:

x \approx - 7.43798 \dots

Apply long division:

\frac{x ^{3} + 6.88916 \dots x ^{2} + 47.34975 \dots x + 382.55000 \dots}{x + 7.43798 \dots} = x^{2} - 0.54882 \dots x + 51.43190 \dots

x^{2} - 0.54882 \dots x + 51.43190 \dots \approx 0

Find one solution for

x^{2} - 0.54882 \dots x + 51.43190 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 7.88916 \dots, x \approx - 7.43798 \dots

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

6527 3^{2} = w^{4} + 4 w^{2}

12 x^{3} - 24 x^{2} + 12 x = 0

What are the solutions to the equation 3018=x^4-x^3-7x^2+9x ?
The solutions to the equation 3018=x^4-x^3-7x^2+9x are x\approx 7.88916…,x\approx-7.43798…
Find the zeros of 3018=x^4-x^3-7x^2+9x
The zeros of 3018=x^4-x^3-7x^2+9x are x\approx 7.88916…,x\approx-7.43798…