#1**+2 **

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

CPhill Oct 20, 2018