If `pa n dq` are chosen randomly from the set `{1,2,3,4,5,6,7,8,9, 10}` with replacement, determine the probability that the roots of the equation `x^2+p x+q=0` are real.

Answer

B

Explanation

The required probability = l - (probability of the event that the roots of `x^2 + px + q =0` are non -real ). The roots of `x^2+px +q =0`
will be non-real if and only if ` p^2-4q lt 0, i.e if p^2 lt 4 q`
The possible values ot'p and q can be possible nccording to the following table.

Therefore, the number of possible pairs = 38 Also, the total number of possible pairs is `10xx 10 =100`
`therefore ` The required probability `=1 -(38)/(100) =1- 0.38 =0.62`