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The coefficients a, b, and c of the quadratic equation a*x² + b*x + c = 0 (where a, b, c are all distinct) are each chosen from the set of the first three prime numbers. If P is the probability that the equation has real roots, what is the value of 18*P?
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- 2
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- 4
Correct answer: 4
Solution
With coefficients chosen from {2, 3, 5} and all distinct, there are 6 permutations. Checking b² - 4ac >= 0 for each reveals the number of favourable cases, from which P and then 18P are found.
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