What are the solutions to the equation y^5+10y^4+100y^3+9.7=1 ?

The solutions to the equation y^5+10y^4+100y^3+9.7=1 are y\approx-0.44963…

Find the zeros of y^5+10y^4+100y^3+9.7=1

The zeros of y^5+10y^4+100y^3+9.7=1 are y\approx-0.44963…

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y^{5} + 10 y^{4} + 100 y^{3} + 9.7 = 1

y \approx - 0.44963 \dots

Solution steps

y^{5} + 10 y^{4} + 100 y^{3} + 9.7 = 1

Multiply both sides by

10

10 y^{5} + 100 y^{4} + 1000 y^{3} + 97 = 10

Move

10

to the left side

10 y^{5} + 100 y^{4} + 1000 y^{3} + 87 = 0

Find one solution for

10 y^{5} + 100 y^{4} + 1000 y^{3} + 87 = 0

using Newton-Raphson:

y \approx - 0.44963 \dots

Apply long division:

\frac{10 y ^{5} + 100 y ^{4} + 1000 y ^{3} + 87}{y + 0.44963 \dots} = 10 y^{4} + 95.50364 \dots y^{3} + 957.05819 \dots y^{2} - 430.32705 \dots y + 193.49018 \dots

10 y^{4} + 95.50364 \dots y^{3} + 957.05819 \dots y^{2} - 430.32705 \dots y + 193.49018 \dots \approx 0

Find one solution for

10 y^{4} + 95.50364 \dots y^{3} + 957.05819 \dots y^{2} - 430.32705 \dots y + 193.49018 \dots = 0

using Newton-Raphson:

No Solution for

y \in R

The solution is

y \approx - 0.44963 \dots

p^{59} p = 30

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

2 x^{4} - 7 x^{3} - 6 x^{2} + 26 x - 12 = 0

16 n^{9} - 25 n^{5} = 0

a^{20} = a 2

What are the solutions to the equation y^5+10y^4+100y^3+9.7=1 ?
The solutions to the equation y^5+10y^4+100y^3+9.7=1 are y\approx-0.44963…
Find the zeros of y^5+10y^4+100y^3+9.7=1
The zeros of y^5+10y^4+100y^3+9.7=1 are y\approx-0.44963…