2008 iTest Problems/Problem 85
Revision as of 20:44, 22 November 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 85 (credit to tenniskidperson3 and official solution) -- system with a hidden form)
Problem
Let be a solution to the system Find the greatest possible value of .
Solution
Note that when multiplying quadratics, terms add up similar to the equations of a system, so let Factoring with the Rational Root Theorem results in . By the Fundamental Theorem of Algebra, we know that are all the linear factors of the polynomial, so the quadratic factors can only be multiplied from these linear factors.
There are only two possible distinct groupings (not counting rearrangements) -- and . In the first case, , and in the second case, . The largest of the two options is .
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 84 |
Followed by: Problem 86 | |
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