4. Find all a such that the equation (x-a) (x - 2x + 3) = 0
a) Has two different solutions
b) Has two positive solutions
c) Has two solutions in the interval [1,3]
d) Has solutions difference between which is greater than 5
(x - a) (x - 2x + 3) = 0
has a solution when x - a = 0 or when x - 2x + 3 = 0.
Let's look at when x - 2x + 3 = 0:
x - 2x + 3 = 0
-x + 3 = 0
3 = x
One of the solutions to the original equation is x = 3. The other is x = ...
In step by step format, this solution solves each of the equations for a in various ways.