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If p and q are chosen randomly from the ...

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

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The correct Answer is:
B
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`
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