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Range of Delta of Quadratic Function

Source: China North MO

August 14, 2006
quadraticsfunctionalgebra unsolvedalgebra

Problem Statement

Given a function f(x)=x2+ax+bf(x)=x^{2}+ax+b with a,b∈Ra,b \in R, if there exists a real number mm such that ∣f(m)∣≤14\left| f(m) \right| \leq \frac{1}{4} and ∣f(m+1)∣≤14\left| f(m+1) \right| \leq \frac{1}{4}, then find the maximum and minimum of the value of Δ=a2−4b\Delta=a^{2}-4b.
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