R: Find roots of polynomial equation

Question

I have this equation in R.

f <- function(x) {first +second*x +third*x^2  +fourth*filter_factor - log(myBITRATE)}

where

first= -5.219078
second = 0.7613156
third = -0.01298033
fourth = -0.05218249
filter_factor = 1
myBITRATE = 184.47

Is there a way to find the roots of this equation?

I need a starting point for the newton-raphson method.

Answer 1

Your function is a second order polynome with one variable, so you can do a trivial calculation:

delta = second^2 - 4*third*(first + fourth*filter_factor - log(myBITRATE))

Since your delta is strictly positive:

x1 = (- second - sqrt(delta))/(2*third)
x2 = (- second + sqrt(delta))/(2*third)

#> x1
#[1] 36.53336
#> f(x1)
#[1] 0
#> x2
#[1] 22.11812
#> f(x2)
#[1] 8.881784e-16