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Suppose p and q are roots of the quadratic equation x² - 3x + a = 0, where a is a real number. Given that p < 1 < q, determine the range of values of a.

1. a < 2
2. a > 2
3. a < 3
4. a > 3

Correct answer: a < 2

Solution

If one root is less than 1 and the other greater than 1, the quadratic (opening upward) must be negative at x = 1, giving f(1) < 0.

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