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 choice from the following answers.
A) 0  B) 3  C) 4  D) 5  E) 6

Rationale: explanation : p + q = α – 2 and pq = – α – 1 ( p + q ) 2 = p 2 + q 2 + 2 pq , thus ( α – 2 ) 2 = p 2 + q 2 + 2 ( – α – 1 ) p 2 + q 2 = α 2 – 4 α + 4 + 2 α + 2 p 2 + q 2 = α 2 – 2 α + 6 p 2 + q 2 = α 2 – 2 α + 1 + 5 p 2 + q 2 = ( α – 1 ) 2 + 5 thus , minimum value of p 2 + q 2 is 5 . answer : d
Answer: D