MathDB
ISI 2024 P2

Source: college entrance

May 12, 2024
algebrapolynomialinequalities

Problem Statement

Suppose n≥2n\ge 2. Consider the polynomial Qn(x)=1−xn−(1−x)n.Q_n(x) = 1-x^n - (1-x)^n . Show that the equation Qn(x)=0Q_n(x) = 0 has only two real roots, namely 00 and 11.
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