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Let f (x) =x ^(2) +2x -t ^(2) and f(x)=0...

Let `f (x) =x ^(2) +2x -t ^(2) and f(x)=0` has two root `alpha (t ) and beta (t) (alpha lt beta)` where t is a real parameter. Let `I (t)=int _(alpha ) ^(beta)f (x)` dx. If the maximum value of `I (t)` be `lamda and | lamda| =p/q` where p and q are relatively prime positive integers. Find the product (pq).

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