suppose a,b,c,d are distinct integers such that (x-a)(x-b)(x-c)(x-d)-4 =0(adsbygoogle = window.adsbygoogle || []).push({});

has a rational root r. Prove that a+b+c+d is a multiple of 4.

I've been trying to solve this for a couple of hours, but except the fact that r is an integer, b/c we have a monic polynomial I didn't get too far.

when we expand we get -(a+b+c+d) x^3 as one of the terms but i'm not sure what to do with it.

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# Rational root

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