Question 14
Let $M$ contain all integers $m$ for which the polynomial
$$2(m-1)x^2-(m^2-m+12)x+6m$$
has either one repeated integer root or two distinct integer roots. Find the number of elements of $M$.
$$2(m-1)x^2-(m^2-m+12)x+6m$$
has either one repeated integer root or two distinct integer roots. Find the number of elements of $M$.