TITLE: roots of quadratic polynomials are positive integer numbers
QUESTION [5 upvotes]: Find positive integer numbers $a,b,c$ such that all the roots of these quadratic polynomials are positive integer numbers
1) $x^2−2ax+b=0$
2) $x^2−2bx+c=0$
3) $x^2−2cx+a=0$
Sorry but I don't know what to do :(( please help me :((

REPLY [2 votes]: Hint:
The trivial case where $a=b=c=1$ gives you the monic polynomial $x^2 - 2x + 1$ which by Descarte's Rule of signs has two positive roots and by rational root theorem has two roots both $x=1$.