MathDB

1

Part of 1980 Dutch Mathematical Olympiad

Problems(1)

1/a < x_0<2/a , x_0 is zero with smallest abs. value f(x) = x^3-ax+1

Source: Netherlands - Dutch NMO 1980 p1

1/28/2023
f(x)=x3−ax+1f(x) = x^3-ax+1 , a∈Ra \in R has three different zeros in RR. Prove that for the zero xox_o with the smallest absolute value holds: 1a<x0<2a\frac{1}{a}< x_0 < \frac{2}{a}
algebrapolynomialinequalities