Question 927517: Find all real values of b such that the equation: x^2 + bx + 6b = 0
only has integer roots.
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! Find all real values of  such that the equation:
 only has integer roots.
Theorem:
Let  , being a quadratic trinomial with integer coefficients  , ,  . Then, both roots or zeros of  are integers; if, and only if,
(i)
The integer  is an integer or perfect square.
and
(ii) The leading coefficient is a divisor of both and .
in your case, The leading coefficient is a divisor of both and because 
but, we need ; so,
 if discriminant  (Positive Discriminant ), we will have Two Real Solutions
 ........solve for
solution is
let have first one greater then :
 ...only has integer roots
proof:
 and  ->solutions are integer roots
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