Polynomials. (1 Viewer)

[TimeGoesTooFast]

Hey guys, need some help and clarification. So you're asked to prove a quadratic has distinct roots- that would just be discussing that the discriminant is greater than 0. How do you go about explaining that a cubic equation and powers beyond have distinct roots? Do you have to relate it back to mutiplicity or sum/product of roots?

 

[qrpw]

Well, a cubic has either 1 or 3 real roots. If it has one, it's obviously distinct. If it has three, you could find stationary points and show that either: one is above the x-axis, one is below (3 distinct roots), or that there is a stationary point on the x-axis (a double root).
I don't think there is a generalization for higher polynomials. Well, in Year 12 4U anyway.

 

[TimeGoesTooFast]

Oh right, completely forgot about that. Thanks for your help