Don’t get me wrong – I am not advocating a cure all technique. I found contentment or peace of find while looking for the roots of a quadratic equation. I’ll like to share it with you.
Suppose you are given a quadratic equation of the form: ax2 + bx + c = 0. In a given quadratic equation with double roots, α and β, one is constrained to work within the confines of given formulas like the sum of the roots and the product of the roots. Whatever other complex derivations you desire, whether in creating a new quadratic equation or playing with the roots, you must work within the confines of the sums and products.
That was what I was doing when I realized one simple truth: if I do this regularly, looking back at my resources, the sums and products of the roots, and only these, in order to create new equations or derivations, teaches me one thing: contentment. I have no other choice. I have only sums and products and no other resource to get to any other equation I desire. I have to control my desires and wishes, be satisfied with what I have before building or deriving anything new.
I wish someone else has a story to tell. Have a class on Tuesday. Been teaching my students matrices. We’ll have determinants next week.