Let p and q be the roots of x 2 – 2x + A = 0 and let r and s be the roots of x 2 – 18x + B = 0. If p < q < r < s are in A.P. then ordered pair (A, B) is equal to -
Text Solution
Verified by ExpertsA
We have p + q = 2, pq = A ………(1)
and r + s = 18, rs = B ………(2)
As p, q, r, s are in AP, we take
P = a – 3d, q = a – d, r = a + d, s = a + 3d
As p < q < r < s, we have d > 0
Now, 2 = p + q = 2a – 4d
And 18 = r + s = 2a + 4d
Solving above equations, we get a = 5 and d = 2
∴ p = – 1, q = 3, r = 7 and s = 11
Thus, A = pq = – 3 and B = rs = 77.
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems