2024 AMC 12B Problems/Problem 17
Problem 17
Integers and are randomly chosen without replacement from the set of integers with absolute value not exceeding . What is the probability that the polynomial has distinct integer roots?
.
Solution 1
, each of has choices
Applying Vieta's formulas,
Cases:
(1) valid
(2) valid
(3) valid
(4) valid
(5) invalid
the total event space is (choice of select a times choice of selecting b given no-replacement)
hence, our answer is
See also
2024 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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