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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 your answers.

 Apr 30, 2019
 #1
avatar+6251 
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all the roots are integers so we havef(x)=(xi1)(xi2)(xi3)(xi4)The constant term is c0=i1i2i3i4=63 can be a root as 32=6On the other hand 3 cannot be a double root as 33=9and there is no combination of integer factors that will multiply 9 to obtain 6

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 May 1, 2019
 #2
avatar+159 
+2

Thank you this response is short and to the point while still helping me understand the problem

 May 2, 2019

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