Integer solution

[kinu]

find all integer value of \(a\) for which the equation \(x^2+ax+6a=0\) has Integer solution

[Rui Carpentier]

Hint:

\(x^2+ax+6=0\Leftrightarrow a=\frac{-x^2}{x+6}\Leftrightarrow a=-x+6-\frac{36}{x+6}\). Thus \(a\) is integer if and only if \(x+6\) divides \(36\).
All you have to do now is to solve the equation \(x+6=d\) for all eighteen interger divisors \(d\) of \(36\), and then you find \(a\).

PS- what your motivation for posting so many problems (most of then difficult). It is hard to believe that all of them are homework sent by the teacher.

[kinu]

Thanks Ruhi Carpenter i have got 4 solution.

actually it is not given by my teacher.

actually it is a question given in my assignment sheet. so at first i have solve myself

and if i have face difficulties then i post here for help

Thanks