When the expression pm2 + qm + 1 is divided by (m – 1), it has a remainder is 4, Find p and q respectively
-
A.
2, -1 -
B.
-1, 2 -
C.
3, -2 -
D.
-2, 3
Correct Answer: Option B
Explanation
pm2 + qm + 1 = (m – 1) Q(x) + 2
p(1)2 + q(1) + 1 = 2
p + q + 1 = 2
p + q = 1…..(i)
pm2 + 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