f(t) = t^5 + t^3 + 2t^2 - 12t + 8

Question

Find all the zeros of the function

Answer 1

To begin, we want to know the possible zeros (also called "roots"), so we can perform the rational root test to find all the possibilities of zeros that this function can have. This is found by dividing the factors of the constant term (in this function, "8" is the constant term) by the factors of the leading term's coefficient (the leading term in this case is t^5 and it's coefficient is 1, since there is no number in front of the term). The possibilities for zeros will then be:

 

+/-1, +/-2, +/-4, +/-8

 

After narrowing down the possible answers, we can perform synthetic division (or polynomial division) and any calculations resulting in a remainder of zero will be an answer (or a "root") of the function.

 

Hope these steps are helpful!

 

Alex