Suppose the polynomial \(f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_2x^2 + a_1x + a_0\)

has integer coefficients, and its roots are distinct integers.

Given that \(a_n=2, \) and \(a_0=66, \) what is the least possible value of \(|a_{n-1}|\)?

abcdefghijklmnopqrst Dec 8, 2021

#1

#2**+5 **

First of all that's not an answer

Second of all, even the lyrics are wrong...

abcdefghijklmnopqrst
Dec 9, 2021

#3**+1 **

The least possible value of |a_{n - 1}| is 26, given by the polynomial 2x^3 - 26x^2 + 38x + 66 = 2(x + 1)(x - 11)(x - 3).

Got it from https://web2.0calc.com/questions/polynomial-roots. It was already asked. LOL!!

AlgebraGuru Dec 9, 2021