if the roots of the equation rx^2 + (r+2)x +3r - 1 = 0 are integers. find all possible rational values of r

Question

there are no other details about my question

Answer 1

Use the quadratic formula with A=r, B=r+2 and C=3r-1. Complete the square under on the expression under the square root sign because it MUST be a perfect square.

You get -11(r-4/11)^2+60/11

Set this expression equal to T where T is an integer.

Then solve for r in terms of T.

 

R =

square-Root[ (60/11-T)/11]+4/11