Question

Let p and q be the roots of x² – 2x + A = 0 and let r and s be the roots of x² – 18x + B = 0. If p < q < r < s are in A.P. then ordered pair (A, B) is equal to -

• A. (– 3, 77)
• B. (77, – 3)
• C. (– 3, – 77)
• D. None

Answer 1

Answer: (A)

(– 3, 77)

Answer 2

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.