Let p and q be the roots of the quadratic equation x^2 - (α-2)x - α - 1 = 0

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?

  1. 0
  2. 3
  3. 4
  4. 5

Answer

Sum of roots = (α - 2)

Product of roots = - (α + 1)

p2 + q2 = (p + q)2 - 2pq

= (α - 2)2 + 2(α + 1)

= α2 - 2α + 6 = (α - 1)2 + 5

Since, minimum value of square can be zero, the minimum possible value of p2 + q2 is 5.

The correct option is D.