3m - m^2 > 0?

Question

solve the quadratic inequality, state the solution using interval notation

Answer 1

That factorises as m(3-m) > 0.

So we need either m and 3-m both > 0, which means 0 or we need m and 3-m both <0, which is impossible.

So 0

Answer 2

m<3

Answer 3

m(3-m) > 0

This means either both m and 3-m are positive or both m and 3-m are negative.

Lets consider the first option

m>0 and 3-m>0. The only values of m satisfying this are the ones in the interval (0,3)


The second option

m<0 and 3-m<0 so m <0 and m>3. Obviously no such m.

So the solution is (0,3)