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Integer Root Illation (Posted on 2016-04-23)

Determine all possible pairs (P,Q) of positive integers such that each of the roots of:
X³ - 17X² + Px - Q² = 0 is an integer.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution

| Comment 2 of 5 |

(In reply to No Subject by armando)

By the rule of signs the equation will have no negative roots.

The sum of the roots is 17 and checking the few possibilities gives four values for roots, P, Q:

(1,8,8), 80, 8

(2,5,10), 80, 10

(3,6,8), 90, 12

(4,4,9), 88, 12

Posted by xdog on 2016-04-24 10:26:19

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