tmua.me Tau Paper 2 · Question 11

A real number $c$ is called admissible if the following equivalence is true for every monic polynomial $p$ of degree $4$ whose derivative has three distinct real roots:

\begin{gathered} p\text{ has four distinct real roots}\\ \Longleftrightarrow\\ (p'(x))^2>c\,p(x)p''(x)\text{ for every real }x. \end{gathered}

Which one of the following is the complete set of admissible values of $c$ ?

1\le c\le\dfrac43

0<c<1

0<c\le1

0<c<\dfrac43

0<c\le\dfrac43

examday

tmua.me Tau Paper 2 · Q11