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x^2 - (2a^2 + 4)x + a^2 + 2a + b = 0

Source: Netherlands - Dutch NMO 1976 p4

January 28, 2023
algebraparameterparameterizationequationtrinomial

Problem Statement

For a,b,x∈Ra,b, x \in R holds: x2−(2a2+4)x+a2+2a+b=0x^2 - (2a^2 + 4)x + a^2 + 2a + b = 0. For which bb does this equation have at least one root between 00 and 11 for all aa?
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