What are the solutions to the equation k^4+2k^3-3k^2-6k+1=0 ?

The solutions to the equation k^4+2k^3-3k^2-6k+1=0 are k\approx 0.15587…,k\approx 1.68491…

Find the zeros of k^4+2k^3-3k^2-6k+1=0

The zeros of k^4+2k^3-3k^2-6k+1=0 are k\approx 0.15587…,k\approx 1.68491…

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k^{4} + 2 k^{3} - 3 k^{2} - 6 k + 1 = 0

k \approx 0.15587 \dots, k \approx 1.68491 \dots

Solution steps

k^{4} + 2 k^{3} - 3 k^{2} - 6 k + 1 = 0

Find one solution for

k^{4} + 2 k^{3} - 3 k^{2} - 6 k + 1 = 0

using Newton-Raphson:

k \approx 0.15587 \dots

Apply long division:

\frac{k ^{4} + 2 k ^{3} - 3 k ^{2} - 6 k + 1}{k - 0.15587 \dots} = k^{3} + 2.15587 \dots k^{2} - 2.66394 \dots k - 6.41525 \dots

k^{3} + 2.15587 \dots k^{2} - 2.66394 \dots k - 6.41525 \dots \approx 0

Find one solution for

k^{3} + 2.15587 \dots k^{2} - 2.66394 \dots k - 6.41525 \dots = 0

using Newton-Raphson:

k \approx 1.68491 \dots

Apply long division:

\frac{k ^{3} + 2.15587 \dots k ^{2} - 2.66394 \dots k - 6.41525 \dots}{k - 1.68491 \dots} = k^{2} + 3.84079 \dots k + 3.80746 \dots

k^{2} + 3.84079 \dots k + 3.80746 \dots \approx 0

Find one solution for

k^{2} + 3.84079 \dots k + 3.80746 \dots = 0

using Newton-Raphson:

No Solution for

k \in R

The solutions are

k \approx 0.15587 \dots, k \approx 1.68491 \dots

x^{4} - (5 + 2) x^{2} + 10 = 0

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

2 x^{3} - 9 x^{2} + 13 x - 6 = 0

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

1 - (p + 3)^{3} = - 8

What are the solutions to the equation k^4+2k^3-3k^2-6k+1=0 ?
The solutions to the equation k^4+2k^3-3k^2-6k+1=0 are k\approx 0.15587…,k\approx 1.68491…
Find the zeros of k^4+2k^3-3k^2-6k+1=0
The zeros of k^4+2k^3-3k^2-6k+1=0 are k\approx 0.15587…,k\approx 1.68491…