2014 AMC 10B Problems/Problem 20
Contents
Problem
For how many integers is the number negative?
Solution 1
First, note that , which motivates us to factor the polynomial as . Since this expression is negative, one term must be negative and the other positive. Also, the first term is obviously smaller than the second, so . Solving this inequality, we find . There are exactly 12 integers that satisfy this inequality, .
Thus our answer is
Solution 2
Since the part of has to be less than (because we want to be negative), we have the inequality --> . has to be positive, so is negative. Then we have . Try answers to find .
See Also
2014 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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