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If pa n dq are chosen randomly from the ...

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.

Text Solution

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The roots of `x^(2) + px + q = 0` will be real if `p^(2) - 4q ge 0` or `p^(2) ge 4q`.
The possible values of p and q are given in the following table:

Also, the total number of possible pairs (p,q) = 10 `xx` 10 = 100
`therefore` Required probability = `(62)/(100) = 0.62`
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