Given that the set a = {x belongs to R | ax2-3x + 2 = 0} (1), if a = an empty set, find the value range of real number a (2) is a single element set, find the value of a and set a (3) Finding the set M = {a belongs to R | A is not equal to an empty set

Given that the set a = {x belongs to R | ax2-3x + 2 = 0} (1), if a = an empty set, find the value range of real number a (2) is a single element set, find the value of a and set a (3) Finding the set M = {a belongs to R | A is not equal to an empty set

I haven't done such a problem for a long time. I don't think it's difficult
(1) A = empty set, which means that the quadratic equation with one variable has no solution, △ B ^ 2-4ac = 9-8a < 0, the range of a is a > 9 / 8
(2) A is a set of single elements, which means that there is only one solution to the quadratic equation with one variable, △ = 9-8a = 0, and a = 9 / 8 is obtained
(3) A is not equal to an empty set, which means that the quadratic equation with one variable has one solution or two solutions, then △≥ 0, a ≥ 9 / 8 is obtained, and the set M = {a ≥ 9 / 8}
I'm not sure whether the answer is correct because I haven't been involved in this exercise for a long time. I hope the above answers can give you some ideas to solve the problem