Question

Using complete sentences, explain how to find the zeros of the function f(x) = 2x^3 – 9x + 3.

Answer 1

Type in the URL of Wolfram Alpha
Type the function the box at top of page and click on the = sign.

Answer 2

There will be three roots. I have no idea how to isolate them when the function is prime.

Answer 3

1st using the remainder theorem find P(0) = 3
next use the remainder theorem again to find P(1) = -4

so a root exists between x = 0 and x = 1

use Newton's method to approximate the roots of a polynomial

\[x _{1} = x _{0} - f(x _{0})/f'(x _{0})\]

let \[x _{0} = 1/2\]

f'(x) = 6x^2 - 9x

f(1/2) =
\[x _{1}\approx 1/2 - (-1.25)/(-7.5)\]

\[x _{1}\approx 1/3\]

another root exists between -2 and -3

P(-2) = 5

P(-3) = -24

axxproximate let x = -2.5 and then use newton's method

Answer 4

The three roots as found by Wolfram are: -2.27163, 0.342241, and 1.92939

Answer 5

a root also exists between P(1) = -4 and P(2) = 1

find an appropriate approximation then use Newton's method again