Probability Question 394
Question: If an integer q be chosen at random in the interval $ -10\le q\le 10, $ then the probability that the roots of the equation $ x^{2}+qx+\frac{3q}{4}+1=0 $ are real is
Options:
A) $ \frac{2}{3} $
B) $ \frac{15}{21} $
C) $ \frac{16}{21} $
D) $ \frac{17}{21} $
Show Answer
Answer:
Correct Answer: D
Solution:
q is an integer, then number of possible outcomes in $ [-10,10]=21 $
Now, for real roots, discriminant $ \ge 0 $
$ \Rightarrow (q-4)(q+1)\ge 0\Rightarrow q\ge 4,q\le -1 $
Then, number of favourable outcomes $ =7+10=17 $
Hence required probability $ =\frac{17}{21} $
BETA
