Discussion

Explanation:

 p2 + q2 = (p + q)2 − 2pq                                 …(i)

 From given equation, p + q = α − 2 and pq = − α − 1

 Substituting values in equation (i), we get,

 p2 + q2 = α2 + 4 − 4α − 2(−α − 1)

= α2 + 4 − 4α + 2α + 2

= α2 − 2α + 1 + 5

= (α − 1)2 + 5

 Minimum value of p2 + q2 will be obtained by putting (α − 1) = 0

 ∴ Minimum value = 5

 Hence, option (d).

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