What are the solutions to the equation x^4+3x^3-12x^2+2x-1=0 ?

The solutions to the equation x^4+3x^3-12x^2+2x-1=0 are x\approx 2.18008…,x\approx-5.32890…

Find the zeros of x^4+3x^3-12x^2+2x-1=0

The zeros of x^4+3x^3-12x^2+2x-1=0 are x\approx 2.18008…,x\approx-5.32890…

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x^{4} + 3 x^{3} - 12 x^{2} + 2 x - 1 = 0

x \approx 2.18008 \dots, x \approx - 5.32890 \dots

Solution steps

x^{4} + 3 x^{3} - 12 x^{2} + 2 x - 1 = 0

Find one solution for

x^{4} + 3 x^{3} - 12 x^{2} + 2 x - 1 = 0

using Newton-Raphson:

x \approx 2.18008 \dots

Apply long division:

\frac{x ^{4} + 3 x ^{3} - 12 x ^{2} + 2 x - 1}{x - 2.18008 \dots} = x^{3} + 5.18008 \dots x^{2} - 0.70699 \dots x + 0.45869 \dots

x^{3} + 5.18008 \dots x^{2} - 0.70699 \dots x + 0.45869 \dots \approx 0

Find one solution for

x^{3} + 5.18008 \dots x^{2} - 0.70699 \dots x + 0.45869 \dots = 0

using Newton-Raphson:

x \approx - 5.32890 \dots

Apply long division:

\frac{x ^{3} + 5.18008 \dots x ^{2} - 0.70699 \dots x + 0.45869 \dots}{x + 5.32890 \dots} = x^{2} - 0.14882 \dots x + 0.08607 \dots

x^{2} - 0.14882 \dots x + 0.08607 \dots \approx 0

Find one solution for

x^{2} - 0.14882 \dots x + 0.08607 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 2.18008 \dots, x \approx - 5.32890 \dots

3 x^{3} + x - 10 = 0

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

14 x^{13} - 14 = 0

x^{3} + 3 x^{2} + 6 x + 5 = 0

4 p^{3} - 28 p^{2} - 31 p - 18 = 0

What are the solutions to the equation x^4+3x^3-12x^2+2x-1=0 ?
The solutions to the equation x^4+3x^3-12x^2+2x-1=0 are x\approx 2.18008…,x\approx-5.32890…
Find the zeros of x^4+3x^3-12x^2+2x-1=0
The zeros of x^4+3x^3-12x^2+2x-1=0 are x\approx 2.18008…,x\approx-5.32890…