Problem
ALG-B1-M10-P007 Parameter
#7
★★☆☆☆ Level 2 of 5
Find all integers \(a\) for which \(x^2+ax+18\) has integer roots.
Use that the product of the roots is \(18\).
Let the roots be \(r,s\). Then \(rs=18\), \(r+s=-a\). Possible sums of factor pairs are \(\pm19,\pm11,\pm9\). Therefore \(a\in\{-19,-11,-9,9,11,19\}\).
Vieta plus divisor checking.