1) Let P(x) be a polynomial such that \(P(x) = P(0) + P(1) x + P(2) x^2\)and P(-1) = 1. Find P(x).

2) Let a,b,c be positive real numbers such that \(\log_a b + \log_b c + \log_c a = 0.\)Find \((\log_a b)^3 + (\log_b c)^3 + (\log_c a)^3.\)

3) Let a,b and c be the roots of \(x^3 - 5x + 7 = 0.\)Find the monic polynomial, in x, whose roots are a - 2, b - 2, and c - 2.

Guest Jun 27, 2019