What do you know about polynomials?
Calculus
Level
4
There are \(n\) polynomials \(\left(P_1(x)..... P_n(x)\right)\) satisfying the following two equations:
\[\begin{align} 8 \cdot P(x) &= (P'(x))^2\cdot P''(x) \\ P(0) &= 4. \end{align}\]
Find the value of \(\displaystyle \sum_{i=1}^n P_i(1).\)
by
Konstantinos Manos