"All limits, especially national ones, are contrary to the nature of mathematics… Mathematics knows no races… For mathematics the whole cultural world is a single country" – David Hilbert. "Face problems with a minimum of blind calculation, a maximum of seeing thought" – Hermann Minkowski
Solving cubics and quartics – video clips
First watch this video (not mine) about sums and products of roots with quadratics:
Then work through this video of mine.
Work through the three examples I do, one by one, pausing after each one.