Let p and q be the roots of the quadratic equation x2 − (α − 2)x − α − 1 = 0. What is the minimum possible value of p2 + q2?
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).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.