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

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