MathDB

12.2

Part of 2003 Moldova National Olympiad

Problems(1)

Properties of derivatives

Source: Moldovan MO 2003

2/21/2006
For every natural number n≥2n\geq{2} consider the following affirmation PnP_n: "Consider a polynomial P(X)P(X) (of degree nn) with real coefficients. If its derivative P′(X)P'(X) has n−1n-1 distinct real roots, then there is a real number CC such that the equation P(x)=CP(x)=C has nn real,distinct roots." Are P4P_4 and P5P_5 both true? Justify your answer.
calculusderivativealgebrapolynomialalgebra proposed