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If the roots of the equation (p-3) x^(2)...

If the roots of the equation `(p-3) x^(2) + 2(p -3) x + 2p-5 =0` are real number distinct for `alpha lt p lt beta and (beta - alpha)` is maximum, then the extreme value of the quadratic expression `-(alpha + beta) x^(2) + alpha beta x+ (alpha -beta)` is

A

OptionA `-(4)/(5)`

B

OptionB 5

C

OptionC `-1`

D

OptionD `(4)/(5)`

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The correct Answer is:
D
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