Determine all possible values of an integer N such that each of the roots of the equation 3X3 - 3X2 + N = 0 is a rational number.
(In reply to the trivial ones
by Ady TZIDON)
Following a lengthy process of solving by a plug-in method
got the following condition to get three real roots
q=N*(9N-4) Should be a non-positive number
N=0 roots 1,0,0
N=4/9 is not an integer, and so are the numbers between
0 and 4/9, the only numbers that would make q negative.
Ergo: N=0 is the only integer answer
the equation may be factored into
and the roots : -1/3, 2/3, 2/3
but rational roots fitting
a non-integer coefficient N
Edited on December 22, 2013, 12:44 pm