Use Newton's method to find all solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations. (Enter your answers as a comma-separated list.)

Question

Use Newton's method to find all solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations. (Enter your answers as a comma-separated list.)

−2x⁷ − 4x⁴ + 9x³ + 6 = 0

Answer 1

Per Decartes rule of signs, there is one sign change, so there is 1 positive solution.

Replacing x with -x:

2x^7 -4x^4 - 9x^3+6

which has2 sign changes.

there are are at most 3 real solutions: 1 positive and 2 negatives

per graphing utility at Desmos dot com, There are in fact 3 real solutions, which

means there are 4 complex imaginary solutions.

They are approximately -1.631, -0.808, and 1.329

The approximate solutions per the Newton's method calculator online at keisan dot casio dot com

-1.630580532826876533028....

-0.8078706984217061156472....

1.329030699429648430497.....