What are the solutions to the equation k^5-3k^3+3k^2-9=16 ?

The solutions to the equation k^5-3k^3+3k^2-9=16 are k\approx 2.08125…

Find the zeros of k^5-3k^3+3k^2-9=16

The zeros of k^5-3k^3+3k^2-9=16 are k\approx 2.08125…

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k^{5} - 3 k^{3} + 3 k^{2} - 9 = 16

k \approx 2.08125 \dots

Solution steps

k^{5} - 3 k^{3} + 3 k^{2} - 9 = 16

Move

16

to the left side

k^{5} - 3 k^{3} + 3 k^{2} - 25 = 0

Find one solution for

k^{5} - 3 k^{3} + 3 k^{2} - 25 = 0

using Newton-Raphson:

k \approx 2.08125 \dots

Apply long division:

\frac{k ^{5} - 3 k ^{3} + 3 k ^{2} - 25}{k - 2.08125 \dots} = k^{4} + 2.08125 \dots k^{3} + 1.33163 \dots k^{2} + 5.77148 \dots k + 12.01195 \dots

k^{4} + 2.08125 \dots k^{3} + 1.33163 \dots k^{2} + 5.77148 \dots k + 12.01195 \dots \approx 0

Find one solution for

k^{4} + 2.08125 \dots k^{3} + 1.33163 \dots k^{2} + 5.77148 \dots k + 12.01195 \dots = 0

using Newton-Raphson:

No Solution for

k \in R

The solution is

k \approx 2.08125 \dots

0.1296 = a^{4}

(x^{2} - 2) (5 x + 3) = 0

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

x^{3} - 7 x^{2} + 8 x - 2 = 0

0 = x^{3} - 2 x

What are the solutions to the equation k^5-3k^3+3k^2-9=16 ?
The solutions to the equation k^5-3k^3+3k^2-9=16 are k\approx 2.08125…
Find the zeros of k^5-3k^3+3k^2-9=16
The zeros of k^5-3k^3+3k^2-9=16 are k\approx 2.08125…