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If the roots of the equation x² - 2ax + a² + a - 3 = 0 are real and both less than 3, then which range of values does 'a' satisfy?

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

Correct answer: a < 2

Solution

Combining all three conditions: D >= 0 gives a <= 3; vertex < 3 gives a < 3; f(3) > 0 gives a < 2 or a > 3. The intersection of {a <= 3} and {a < 3} and {a < 2 or a > 3} is a < 2.

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