A quadratic equation x2 + bx + c = 0 has two real roots. If the difference between the reciprocals of the roots is 1/3, and the sum of the reciprocals of the squares of the roots is 5/9, then the largest possible value of (b + c) is
Explanation:
Let the roots of the given quandratic equation be p and q.
⇒ 1p-1q = 13 ...(1)
⇒ 1p2+1q2 = 59 ...(2)
Squaring (1) we get
⇒ 1p2+1q2-2pq = 19
⇒ 59-2pq = 19
⇒ pq = 9/2 = c
From (2) we get
⇒ 9(p2 + q2) = 5p2q2
⇒ 9(p2 + q2) = 5(pq)2
⇒ 9((p + q)2 - 2pq) = 5(9/2)2
⇒ (p + q)2 - 9 = 45/4
⇒ (p + q)2 = 81/4
⇒ (p + q) = ± 9/2 = - b
largest possible value of b = 9/2
∴ Largest possible value of a + b = 9/2 + 9/2 = 9.
Hence, 9.
» 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.