If (x – 2) and (x + 1) are factors of the expression x3 + px2 + qx + 1, what is the sum of p and q
-
A.
9 -
B.
-3 -
C.
3 -
D.
(frac{17}{3}) -
E.
(frac{2}{3})
Correct Answer: Option B
Explanation
x3 + px2 + qx + 1 = (x – 1) Q(x) + R
x – 2 = 0, x = 2, R = 0,
4p + 2p = -9……..(i)
x3 + px2 + qx + 1 = (x – 1)Q(x) + R
-1 + p – q + 1 = 0
p – q = 0…….(ii)
Solve the equation simultaneously
p = (frac{-3}{2})
q = (frac{-3}{2})
p + q = (frac{3}{2}) – (frac{3}{2})
= (frac{-6}{2})
= -3