What are the solutions to the equation y^7+y^2-8=0 ?

The solutions to the equation y^7+y^2-8=0 are y\approx 1.30096…

Find the zeros of y^7+y^2-8=0

The zeros of y^7+y^2-8=0 are y\approx 1.30096…

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y^{7} + y^{2} - 8 = 0

y \approx 1.30096 \dots

Solution steps

y^{7} + y^{2} - 8 = 0

Find one solution for

y^{7} + y^{2} - 8 = 0

using Newton-Raphson:

y \approx 1.30096 \dots

Apply long division:

\frac{y ^{7} + y ^{2} - 8}{y - 1.30096 \dots} = y^{6} + 1.30096 \dots y^{5} + 1.69250 \dots y^{4} + 2.20189 \dots y^{3} + 2.86458 \dots y^{2} + 4.72671 \dots y + 6.14928 \dots

y^{6} + 1.30096 \dots y^{5} + 1.69250 \dots y^{4} + 2.20189 \dots y^{3} + 2.86458 \dots y^{2} + 4.72671 \dots y + 6.14928 \dots \approx 0

Find one solution for

y^{6} + 1.30096 \dots y^{5} + 1.69250 \dots y^{4} + 2.20189 \dots y^{3} + 2.86458 \dots y^{2} + 4.72671 \dots y + 6.14928 \dots = 0

using Newton-Raphson:

No Solution for

y \in R

The solution is

y \approx 1.30096 \dots

x^{4} - 7 x^{2} + x^{3} - x + 4 = 0

x^{5} - 9 x^{4} + 15 x^{3} + 25 x^{2} = 0

0 = 12 x^{3} - 48 x^{2} + 36 x

x^{4} + 8 x^{3} + 14 x^{2} - 2 x + 1 = 0

m^{3} + m^{2} + 4 m + 4 = 0

What are the solutions to the equation y^7+y^2-8=0 ?
The solutions to the equation y^7+y^2-8=0 are y\approx 1.30096…
Find the zeros of y^7+y^2-8=0
The zeros of y^7+y^2-8=0 are y\approx 1.30096…