How are the parameters in GLM's linear predictor calculated

How are the parameters (alpha, beta1, beta2 etc) in GLM's linear predictor calculated?

 

But the study material has not given an example of solving the parameters using MLE. So it's not important for exams?

 

There are many questions of deriving MLE of GLM and estimating parameters in past papers. So, I think this is very important. Have a look to past years papers, you will get the idea. In chapter, an example of deriving equations of MLE is given on pg31.
To see more examples, refer to past papers.