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?
- 0
- 3
- 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.