Question

Diane loves coasters that dip into tunnels during the ride.Her favorite coaster is modeled by h(t)=2t +23t-59t+24. Using rational route theorem, what are the possible rational zeros for the function

Answer 1

The possible rational zeros for the function are

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/2, ±3/2

Explanation:

I believe that there is an error in the function with the exponents, it must be:

`h(t) = 2t^(3) + 23t^(2)+59t+24`

If this is the function that you need, then we must use the rational zero theorem. It says that if a polynomial function, written in descending order of the exponents, has integer coefficients, then any rational zero must be of the form ± p/ q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Thus

In this case the constant term is 24 and then

p = ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

The factor of the leading coefficient is 2, thus

q = ±1, ±2

The possible rational zeros for the function are

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/2, ±3/2