If x – 1 and x + 1 are both factors of the equation x(^3) + px(^2) + qx + 6 = 0, evaluate p and q
-
A.
-6, -1 -
B.
6, 1 -
C.
1, -1 -
D.
6, -6
Correct Answer: Option A
Explanation
(x^{3} + px^{2} + qx + 6 = 0)
f(x – 1) = 0; f(1) = 0.
(1^{3} + p(1^{2}) + q(1) + 6 = 0 implies p + q = -7 … (1))
f(x + 1) = 0; f(-1) = 0.
((-1)^{3} + p(-1^{2}) + q(-1) + 6 = 0 implies p – q = -5 … (2))
Subtract (2) from (1).
(2q = -2 implies q = -1)
(p – (-1) = -5 implies p = -5 – 1 = -6)
((p, q) = (-6, -1))