The root finding algorithm goes through the same number of iterations either with 1st degree or the 2nd degree polynomial and returns the roots that converge faster using the 1st degree approximation as compared to the 2nd degree approximation.

Any thoughts on why this is occurring?

As an example:

IRR [ -100,50,40,30,10 ]

Seed value = 0.10

Solving for interest rate in 1st degree Taylor polynomial approximation

IRR = 0.14488783107567296

Solving for interest rate in 2nd degree Taylor polynomial approximation

IRR 1 = null

IRR 2 = 0.14488785866378917