MathDB
P,Q

Source: Iran 2005

August 27, 2005
functionratioalgebra proposedalgebra

Problem Statement

Suppose P,Q∈R[x]P,Q\in \mathbb R[x] that deg P=deg Qdeg\ P=deg\ Q and PQ′−QP′PQ'-QP' has no real root. Prove that for each λ∈R\lambda \in \mathbb R number of real roots of PP and λP+(1−λ)Q\lambda P+(1-\lambda)Q are equal.
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