Quote:
Originally Posted by Aaron W.
That looks like a complete mess to me. They switched to their non-standard sigma notation and then called it something that it almost certainly cannot be.
Just to help out a little here, their notation is a bit wonky. But when they talk about "sum of possible roots," etc. They're referring to things like Vieta's formulas.
For example, take the equation
$$x^7 + 9x - 3.$$
I don't care WHAT the roots are, but I can tell you that their product is $3.$ How can I do that? Well, we know this must factor as
(x - blah)(x-blah)(x-blah)(x-blah)(x-blah)(x-blah)(x-blah)
Where "blah" are the roots. When you multiply that all out, the constant term is just the product of all the (-blah)'s. That's means you can find the product of the roots by looking at the constant term.
Similarly, you can find the sum of the roots from one of the terms (I won't tell you which, think about it -- you want only one root at a time, none multiplied together, so that might help -- or just look at some examples).