Similar to ARML 2010 Team Problem 9 Cubic Vieta. 0 coefficient of x^2 implies minus the sum of the roots is equals zero. 0 coefficient of x implies sum of the product of the root pairs are equal to 0.(Sometimes called second degree elementary symmetric polynomial) The alternate solution posted in solution manual was supper clever exploiting the commutative property of multiplication.
Profuse thanks to Paul J. Karafiol for being a big part the excellently written and organized AMERICAN REGIONS MATH LEAGUE
&
Power & Local Contests
2009-2014 document
Also gratitude to problem writer Andy Niedermaier
I also wonder if winner Ben Gunby solved this problem the "easy way" with the clever trick presented in the alternate solution?
Негізгі бет x^3+ ax +372 and x^3 +bx^2 +961/12 have two common roots. Find the product of the common roots
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