Problem of the month for April 2013: Apr 12, 2013

Consider the polynomial function p(x) = x^5 - x + 1. a) How many real zeroes does p have? Bound each of these by their nearest integers. Justify your answer analytically (i.e., without calculator or computer). b) Let a be the smallest real zero of p. Rationalize the denominator of 1/ (a + 2). Figure it out? Speak with Professor Herschkorn, he'll be happy to know.