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sum of the squares of the coeficients of the P(x)Q(x)

Source: All-Russian olympiad 1995, Grade 10, Second Day, Problem 8

October 20, 2013

algebrapolynomial

Problem Statement

Let

P(x)

and

Q(x)

be monic polynomials. Prove that the sum of the squares of the coeficients of the polynomial

P(x)Q(x)

is not smaller than the sum of the squares of the free coefficients of

P(x)

and

Q(x)

. A. Galochkin, O. Ljashko