SOLUTION: Find all real values of b such that the equation: x^2 + bx + 6b = 0 only has integer roots.

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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