Let `pa n dq` be the roots of the equation `x^2-2x+A=0` and let `ra n ds` be the roots of the equation `x^2-18 x+B=0.If p

Options

A. A = 3, B = 77
B. A = -3, B = 77
C. A = 3, B = - 17
D. none of these

Answer

B

Explanation

Let `p = a - 3d, q = a -d, r = a + d and s = s = a + 3d`, where d `gt` 0.
Since p, q are the roots of `x^(2) - 2x + A = 0`
`therefore" "p + q = 2 and pq = A`
It is given that r and s are the roots of `x^(2) - 18x + B = 0`.
`therefore" "r+s =18 and rs =B`.
Now, `p + q = 2 and r + s = 18`
`rArr" "2a - 4d = 2 and 2a + 4d = 18`
`rArr" "a-2d = 1 and a + 2d = 9`
`rArr" "a = 5, d = 2 rArr p = -1, q = 3, r = 7 and s = 11`
`therefore" "A = pq = - 3, and B = rs = 77`.