jmc

Question

A polynomial with integer coefficients is of the form x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 18.You are told that the integer r is a double root of this polynomial. (In other words, the polynomial is divisible by (x - r)^2.) Enter all the possible values of r, separated by commas.

Accepted Answer

By the Integer Root Theorem, an integer root must divide the constant term. In this case, r^2 must divide 18. Thus, the only possible values of r are -3,-1,1,3.