1. ## series

given that An,An-1, .....A1,A0 are all integers and An and A0 are nonzero,derive a necessary condition for the equation AnX^n +An-1X^n-1+......+A1X+A0=0 to have a rational root.then use this condition to prove that (n-1)^1/2 + (n+2)^1/2 is irrational for every integer n>=1

2. Originally Posted by dinny4001

given that An,An-1, .....A1,A0 are all integers and An and A0 are nonzero,derive a necessary condition for the equation AnX^n +An-1X^n-1+......+A1X+A0=0 to have a rational root.

then use this condition to prove that (n-1)^1/2 + (n+2)^1/2 is irrational for every integer n>=1
i guess you meant $\displaystyle \sqrt{n-1} + \sqrt{n+1}$? and do you know the rational root theorem?

3. nope...i dont remeber it..its my first course in advance math