MathDB

Two polynomials

f(x)

and

g(x)

with real coefficients are called similar if there exist nonzero real number a such that

f(x) = q \cdot g(x)

for all

x \in R

. I. Show that there exists a polynomial

P(x)

of degree 1999 with real coefficients which satisfies the condition:

(P(x))^2 - 4

and

(P'(x))^2 \cdot (x^2-4)

are similar. II. How many polynomials of degree 1999 are there which have above mentioned property.

Problem Statement