Mathegoras

Complex numbers › The complex plane › Extremes of the modulus

Maximum of |bc| for a bounded quadratic

High school · ●●●●● 200 pts

Let complex numbers aa, bb, cc satisfy: for any complex number zz with ∣z∣≤1|z|\leq 1, we have ∣az2+bz+c∣≤1|az^2+bz+c|\leq 1. Find the maximum value of ∣bc∣|bc|. Round to two decimal places.

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polynomial inequalitiesoptimizationAM-GM inequality