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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.

 Aug 11, 2019
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"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.

 Aug 11, 2019

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