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If x - 1 and x + 1 are both factors of the equation x3 ...

If x - 1 and x + 1 are both factors of the equation x3 + px2 + qx + 6 = 0, evaluate p and q

A.

-6, -1

B.

6, 1

C.

1, -1

D.

6, -6

Correct answer is A

x3+px2+qx+6=0

f(x - 1) = 0; f(1) = 0.

13+p(12)+q(1)+6=0p+q=7...(1)

f(x + 1) = 0; f(-1) = 0.

(1)3+p(12)+q(1)+6=0pq=5...(2)

Subtract (2) from (1).

2q=2q=1

p(1)=5p=51=6

(p,q)=(6,1)