I'm writing an essay on Radicals and one of my questions is on symmetries and I was hoping someone would have a bit of insight or could maybe help me reword the question so I undertsand what is being asked!
For example, I have some research on Galois theory and Newton's theorem on symmetric functions but nothing particularly relevant and I'm struggling to find relevant subject matter or revision materials that's specific to my question.
The actual question is :
Start discussing the role of symmetries in solving quadratics: interchanging the two roots amounts to multiplying a square root by -1.
EDIT: That is literally the only information I was given on the question, which I think is a reason I'm so confused.
I think I'm mainly thrown off by the wording and am unsure as to how to approach it, as well as being generally confused as to what it means by interchanging the roots amounts to mutiplying a square root by -1, and how that causes for discussion?
I'm not at all asking for any massive answers or for people to do my work for me but if anyone had any advice or even some links to any online material I would be so so grateful :)