+128472 The discriminant is
(m - 2)^2 - 4m (m - 3)
To have multiple roots....this must be a perfect square > 0
(m - 2)^2 - 4m (m - 3) simplify
m^2 - 4m + 4 - 4m^2 + 12m
-3m^2 + 8m + 4
Graphing this.....it is only > 0 when the integer values for m = 0, 1, 2 or 3
There are two values for m that produce a perfect square
When m = 1.....the perfect square is 9
When m = 3, the perfect square is 1
So....one possible quadratic is
x^2 + x - 2 factoring we have (x + 2) (x - 1) and the roots are -2 and 1
The other possible quadratic is
3x^2 - x factor x (3x - 1) and the roots are 0 and 1/3
However....we require integer roots...so
x^2 + x - 2 is the quadratic and m = 1
