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)?

(b) Is it possible for x=3 to be a double root of f(x)?

Prove the answer.

I really help and ASAP, please answer this for me. I do not understand this problem at all.

Guest Aug 11, 2019

#1**+1 **

"*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.

Alan Aug 11, 2019