Problem
ALG-B1-M03-P014 Integer Roots with a Parameter
#14
★★★☆☆ Level 3 of 5
Find all integers \(a\) for which \(x^2-ax+12=0\) has two integer roots.
The roots must be integer divisors of \(12\).
Let the roots be \(m,n\). Then \(mn=12\), \(m+n=a\).
List integer divisor pairs: \((1,12)\), \((2,6)\), \((3,4)\), and the corresponding negative pairs. Thus \(a=13,8,7,-13,-8,-7\).
The parameter is reduced to divisor pairs.