Quadratic equations: x^2-5x+4=0 and x^2-(a+2)x+1=0

[Alfredo]

We have x^2-5x+4=0 and x^2-(a+2)x+1=0
For wich values of a the two equations have at least
a common solution.

 

[ksdhart2]

Well, since you've shown no work of your own, I'm forced to assume that's because you're stuck at the very beginning and have none to show. So, a good first step is to start with the definitions involved. What does it mean, algebraically, for these two quadratic functions to "have at least one common solution?" What does it mean in terms of the graphs of these functions? How does that help you solve the problem?

 

[stapel]

We have x^2-5x+4=0 and x^2-(a+2)x+1=0
For which values of a the two equations have at least a common solution.

How did your book and your instructor solve similar exercises? If you had two linear equations, each equal to the same thing, how would you solve that system? Do the same thing here. Where does this lead?

Please be complete, showing all of your steps and reasoning. Thank you!