5

Part of 2000 India National Olympiad

Problems(1)

Solution of a cubic

Source: INMO 2000 Problem 5

a,b,c

be three real numbers such that

1 \geq a \geq b \geq c \geq 0

. prove that if

\lambda

is a root of the cubic equation

x^3 + ax^2 + bx + c = 0

(real or complex), then

| \lambda | \leq 1.

algebrapolynomialalgebra unsolved