Statistics And Probability Question 531
Question: If a is an integer lying in [ $ - $ 5, 30], then the probability that the graph $ y=x^{2}+2,(a+4)x-5a+64 $ is strictly above the x-axis is
Options:
A) 1/6
B) 7/36
C) 2/9
D) 3/5
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ x^{2}+2(a+4)x-5a+64\ge 0 $ If $ D\le 0 $ , then $ {{(a+4)}^{2}}-(-5a+64)<0 $ Or $ a^{2}+13a-48<0 $ Or $ (a+16)(a-3)<0 $
$ \Rightarrow -16<a<3\Leftrightarrow -5\le a\le 2 $ Then, the favorable cases is equal to the number of integers in the interval [ $ - $ 5, 2], i.e., 8. Total number of cases is equal to the number of integers in the interval [ $ - $ 5, 30], i.e., 36. Hence, the required probability is 8/36=2/9.
BETA
