Given that f(x) is a polynomial of degree EIGHT such that
f(t) = 1/t for t = 1,2,3,4,5,...,9
Find f(10)
let so is a polynomial of degree 9 with 9 roots t = 1, 2, ... , 9. thus
for some constant now in (1) put t = 0 to to get: therefore (1) becomes:
finally in (2) put t = 10 to get: which gives us:
Remark: it's clear that the problem can be easily generalized in different ways and the above method will still work quite nicely!