6 votes

Finding the range of $\frac{5 \cos x-2 \sin ^{2} x+4 \sin x-3}{6|\cos x|+1}$

If $x\in[-\pi/2,\pi/2]$ then $|\cos x|=\cos x$ so \begin{equation} \frac{5 \cos x-2 \sin ^{2} x+4 \sin x-3}{6|\cos x|+1} ={5\cos x+5/6\over6\cos x+1}+{-2\sin^2 x+ 4\sin x -3\frac56\over6\cos x+1}\\ =5/...
user avatar
  • 8,135
1 vote
Accepted

An interesting problem having uneasy answers

Try to form quadratica in all variables then apply the condition of real roots. You will get values of all variables having upper and lower bound.
user avatar
  • 1,299
1 vote
Accepted

Nature of $\Delta$ in polynomials$?$

As pointed in the comments, for higher degree polynomials discriminant does not carries all the information.Discriminant becomes more and more complex as you go higher and higher. And you should try ...
user avatar
  • 1,299
1 vote

Question from IOQM 2021 based on functions

$p(x)=\frac{4}{x}$ is not a polynomial, so it cannot be the answer to this question. Instead, the idea of the solution is based around the minimal polynomial, the smallest degree polynomial $m(x)$ ...
user avatar
  • 4,645

Only top scored, non community-wiki answers of a minimum length are eligible