I found out where my mistake was! Thank you!

Also, for 5b, what kind of question is this? Why was b^2 -4ac involved?

This question is actuallyg doing the reverse of your discriminent, to prove something always positive , you must prove that the discriminent is negative

So if something is always negative, is the discriminent always positive?

When an equation is always negative or positive, the discriminent is always less than 0. Since in this qn the discriminent is a something^2, and we managed to factorise out the negative sign, it means that our discriminent is negative, and because the m and n are unknowns(meaning that we can't prove it's negative) so therefore the eqn is always positive(to prove the ans)