Let p and q be the root of the quadratic equation x2 - (∝ - 2)x - ∝ -1 =0. what is the minimum possible value of p2 + q2 ?  Choose the correct option.
A) 0 B) 3 C) 4 D) 5 E) 6
Explanation :   p + q = α –2 and pq = –α – 1   (p + q)2 = p2 + q2 + 2pq,   Thus (α –2)2 = p2 + q2 + 2(–α – 1)   p2 + q2 = α2 – 4α + 4 + 2α + 2   p2 + q2 = α2 – 2α + 6   p2 + q2 = α2 – 2α + 1 + 5   p2 + q2 = (α – 1)2 + 5   Thus, minimum value of p2 + q2 is 5.   Answer : 5
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Let p and q be the root of the quadratic equation x2 - (∝ - 2)x - ∝ -1 =0. what is the minimum possible value of p2 + q2 ?