"Let f(x) be a quartic polynomial with integer coefficients and four integer roots. Suppose the constant term of f(x) is 6.
(a) Is it possible for x=3 to be a root of f(x)?"
(a) (x+1)2(x-2)(x-3) constant term is 6
"(b) Is it possible for x=3 to be a double root of f(x)?"
(x-3)2(x-a)(x-b) constant term is 9ab Therefore not possible for this to be 6 if a and b are integers.