When the expression pm\(^2\) + qm + 1 is divided by (m – 1), it has a remainder is 2, and when divided by (m + 1), the remainder is 4. Find p and q respectively
- 2, -1
-
-1, 2
- 3, -2
- -2, 3
The correct answer is: B
Explanation
pm\(^2\) + qm + 1 = (m - 1) Q(x) + 2, where Q(x) = remainder.
p(1)\(^2\) + q(1) + 1 = 2
p + q + 1 = 2
p + q = 1.....(i)
pm\(^2\) + qm + 1 = (m - 1)Q(x) + 4
p(-1)\(^2\) + q(-1) + 1 = 4
p - q + 1 = 4
p - q = 3....(ii)
p + q = 1, p - q = -3
2p = -2, p = -1
-1 + q = 1
q = 2