Find all zeros: #f(x)=3x^7-32x^6+28x^5+591x^4-1181x^3-2810x^2+5550x-1125#?

1 Answer
Dec 29, 2017

I don't have time to give a detailed explanation, but the zeroes are #x=5# (multiplicity 3), #x=-3# (multiplicity 2), and #x=(5 pm sqrt{13})/6# (each of multiplicity 1).


You could use your calculator to help you guess some roots (zeros), and then try synthetic division to help you confirm this, as well as factor the polynomial until you ultimately use the quadratic formula to help you find the last two zeros.

It's not as well-known these days, but in the past (before graphing calculators) they also would have used the Rational Root Theorem as a way to guess possible rational roots.