Question
Mon February 13, 2012 By: Ajinkya Pande

Each coefficient in equation ax^2+bx+c=0 is obtained by throwing a fair die.Find the probability that the equation have real roots

Expert Reply
Mon February 13, 2012
For real roots b2 >= 4ac
We can observedifferent cases ,
1) For a =1
If c = 1 , b can have any value from 2 to 6
If c = 2 , b can have any value from 3 to 6
If c = 3 , b can have any value from 4 to 6
If c = 4 , b can have any value from 4 to 6
If c = 5 , b can have any value from 5 to 6
If c = 6 , b can have any value from 5 to 6
2) For a = 2
If c = 1 , b can have any value from 3 to 6
If c = 2 , b can have any value from 4 to 6
If c = 3 , b can have any value from 5 to 6
If c = 4 , b can have any value 6
Similarly we can find different cases for a = 3 , 4, 5 , 6
Probability = No of outcomes in this event / Total possible outcomes
= (5 + 4 + 3 + 3 + 2 + 2 + 4 + 3+ 2+ 1+ 3+2+1+3+1+2+2)/216
= 43/216
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