1979 AHSME Problems/Problem 27
Problem 27
An ordered pair of integers, each of which has absolute value less than or equal to five, is chosen at random, with each such ordered pair having an equal likelihood of being chosen. What is the probability that the equation will not have distinct positive real roots?
Solution
There are cases where the roots are real, positive and distinct. The roots to the quadratic equation are .
In order for we certainly need . Additionally, for the roots to be both real and distinct we need . And lastly, for both roots to be positive we need . Combining these inequalities we determine that and .
This leaves just cases which can easily be checked by hand.
The answer is
See Also
1979 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 26 |
Followed by Problem 28 | |
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