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(x^2 + ax + 4)(x^2 - 5x + 6) < 0, set of solutions is interval

Source: 2006 Austria Beginners' Competition p2

October 12, 2022
algebrainequalities

Problem Statement

For which real numbers aa is the set of all solutions of the inequality (x2+ax+4)(x2āˆ’5x+6)<0(x^2 + ax + 4)(x^2 - 5x + 6) < 0 an interval?
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