What are the solutions to the equation z^4-11z^3+14z^2-11z+12=0 ?

The solutions to the equation z^4-11z^3+14z^2-11z+12=0 are z\approx 1.30227…,z\approx 9.65458…

Find the zeros of z^4-11z^3+14z^2-11z+12=0

The zeros of z^4-11z^3+14z^2-11z+12=0 are z\approx 1.30227…,z\approx 9.65458…

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z^{4} - 11 z^{3} + 14 z^{2} - 11 z + 12 = 0

z \approx 1.30227 \dots, z \approx 9.65458 \dots

Solution steps

z^{4} - 11 z^{3} + 14 z^{2} - 11 z + 12 = 0

Find one solution for

z^{4} - 11 z^{3} + 14 z^{2} - 11 z + 12 = 0

using Newton-Raphson:

z \approx 1.30227 \dots

Apply long division:

\frac{z ^{4} - 11 z ^{3} + 14 z ^{2} - 11 z + 12}{z - 1.30227 \dots} = z^{3} - 9.69772 \dots z^{2} + 1.37093 \dots z - 9.21467 \dots

z^{3} - 9.69772 \dots z^{2} + 1.37093 \dots z - 9.21467 \dots \approx 0

Find one solution for

z^{3} - 9.69772 \dots z^{2} + 1.37093 \dots z - 9.21467 \dots = 0

using Newton-Raphson:

z \approx 9.65458 \dots

Apply long division:

\frac{z ^{3} - 9.69772 \dots z ^{2} + 1.37093 \dots z - 9.21467 \dots}{z - 9.65458 \dots} = z^{2} - 0.04313 \dots z + 0.95443 \dots

z^{2} - 0.04313 \dots z + 0.95443 \dots \approx 0

Find one solution for

z^{2} - 0.04313 \dots z + 0.95443 \dots = 0

using Newton-Raphson:

No Solution for

z \in R

The solutions are

z \approx 1.30227 \dots, z \approx 9.65458 \dots

x^{4} + 6 x^{3} + 6 x^{2} + 6 x + 5 = 0

a, a^{5} = b^{4}

x^{3} - x + 1 = 0

x^{4} - 16 x^{2} = 0

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

What are the solutions to the equation z^4-11z^3+14z^2-11z+12=0 ?
The solutions to the equation z^4-11z^3+14z^2-11z+12=0 are z\approx 1.30227…,z\approx 9.65458…
Find the zeros of z^4-11z^3+14z^2-11z+12=0
The zeros of z^4-11z^3+14z^2-11z+12=0 are z\approx 1.30227…,z\approx 9.65458…