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

The solutions to the equation x^4-4x^3+x^2-5x=3 are x\approx-0.46610…,x\approx 4.09737…

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

The zeros of x^4-4x^3+x^2-5x=3 are x\approx-0.46610…,x\approx 4.09737…

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

x \approx - 0.46610 \dots, x \approx 4.09737 \dots

Solution steps

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

Move

3

to the left side

x^{4} - 4 x^{3} + x^{2} - 5 x - 3 = 0

Find one solution for

x^{4} - 4 x^{3} + x^{2} - 5 x - 3 = 0

using Newton-Raphson:

x \approx - 0.46610 \dots

Apply long division:

\frac{x ^{4} - 4 x ^{3} + x ^{2} - 5 x - 3}{x + 0.46610 \dots} = x^{3} - 4.46610 \dots x^{2} + 3.08165 \dots x - 6.43636 \dots

x^{3} - 4.46610 \dots x^{2} + 3.08165 \dots x - 6.43636 \dots \approx 0

Find one solution for

x^{3} - 4.46610 \dots x^{2} + 3.08165 \dots x - 6.43636 \dots = 0

using Newton-Raphson:

x \approx 4.09737 \dots

Apply long division:

\frac{x ^{3} - 4.46610 \dots x ^{2} + 3.08165 \dots x - 6.43636 \dots}{x - 4.09737 \dots} = x^{2} - 0.36872 \dots x + 1.57085 \dots

x^{2} - 0.36872 \dots x + 1.57085 \dots \approx 0

Find one solution for

x^{2} - 0.36872 \dots x + 1.57085 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.46610 \dots, x \approx 4.09737 \dots

x^{7} - 6 x^{5} - x^{2} + x - 7 = 0

2 (x^{2} - 100) (36 x^{2} - 49) = 0

6 x^{4} - 9 x^{3} = 0

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

6 x^{4} - 5 x^{2} - 1 = 0

What are the solutions to the equation x^4-4x^3+x^2-5x=3 ?
The solutions to the equation x^4-4x^3+x^2-5x=3 are x\approx-0.46610…,x\approx 4.09737…
Find the zeros of x^4-4x^3+x^2-5x=3
The zeros of x^4-4x^3+x^2-5x=3 are x\approx-0.46610…,x\approx 4.09737…