What are the solutions to the equation a-2a^5=3 ?

The solutions to the equation a-2a^5=3 are a\approx-1.15761…

Find the zeros of a-2a^5=3

The zeros of a-2a^5=3 are a\approx-1.15761…

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a - 2 a^{5} = 3

a \approx - 1.15761 \dots

Solution steps

a - 2 a^{5} = 3

Move

3

to the left side

a - 2 a^{5} - 3 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 2 a^{5} + a - 3 = 0

Find one solution for

- 2 a^{5} + a - 3 = 0

using Newton-Raphson:

a \approx - 1.15761 \dots

Apply long division:

\frac{- 2 a ^{5} + a - 3}{a + 1.15761 \dots} = - 2 a^{4} + 2.31522 \dots a^{3} - 2.68012 \dots a^{2} + 3.10254 \dots a - 2.59154 \dots

- 2 a^{4} + 2.31522 \dots a^{3} - 2.68012 \dots a^{2} + 3.10254 \dots a - 2.59154 \dots \approx 0

Find one solution for

- 2 a^{4} + 2.31522 \dots a^{3} - 2.68012 \dots a^{2} + 3.10254 \dots a - 2.59154 \dots = 0

using Newton-Raphson:

No Solution for

a \in R

The solution is

a \approx - 1.15761 \dots

- x^{3} + 7 x^{2} - 15 x + 9 = 0

x^{10} = 1

x^{10} = 2

x (x + 2)^{3} - 15 (x + 2)^{2} = 0

- x^{3} + 3 x^{2} + 5 x - 2 = 0, x

What are the solutions to the equation a-2a^5=3 ?
The solutions to the equation a-2a^5=3 are a\approx-1.15761…
Find the zeros of a-2a^5=3
The zeros of a-2a^5=3 are a\approx-1.15761…