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Q.

If α,β are the roots of the quadratic equation, x2−2p(x−4)−15=0, then the greatest integer p for which one root is less than 1 and the other root is greater than 2 is?

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answer is 2.

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Detailed Solution

For one root to be less than 1 and other to be greater than 2, P(1) < 0 and P(2) < 0

Hence p<73 & p<114, which implies p<73. Greatest integral values of p is 2.

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