The examples gone through today are on math google site, in case you did not manage to take down notes. The file name is "Examples 16-20 (pg 24) of Notes Chapter A02.pdf" Read through the examples and understand. Then attempt the homework: Assignment A02c (pg 31 of thick notes) Q1.
If you tried filling in the table in example 15 on page 23, you may check your answer with the document "2.3 Discriminant and Nature of Roots.pdf" on the google site
For more advanced inequalities questions, you may refer to Examples 13d and 13e in the file "Examples 13-15 (pg 20) of Notes Chapter A02.pdf".
I have posted a thread on imaginary numbers on the "math" page of this blog. For your reading pleasure.