SOLUTION: Determine if the polynomial below is irreducible over Q(rationals) t^5

SOLUTION: Determine if the polynomial below is irreducible over Q(rationals) t^5 - 15t^4 + 18t^2 -12

Question 31163: Determine if the polynomial below is irreducible over Q(rationals)
t^5 - 15t^4 + 18t^2 -12
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Determine if the polynomial below is irreducible over Q(rationals)
t^5 - 15t^4 + 18t^2 -12
THE RULE FOR EXISTENCE OF RATIONAL ROOTS IS
P/Q WILL BE A ROOT ONLY IF P IS A FACTOR OF CONSTANT TERM (-12 HERE)AND Q IS A FACTOR OF HIGHEST DEGREE TERM'S COEFFICIENT (1 HERE)
SO ONLY POSSIBLE RATIONAL ROOTS ARE 1,2,3,4,6,12,-1,-2,-3,-4,-6,-12......
WE FIND THAT NONE OF THEM YIELD A ZERO THAT IS F(1)..OR..F(2)....ETC ARE NOT ZERO.HENCE THERE ARE NO RATIONAL ROOTS FOR THIS EQN.
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