JAMB - Mathematics (1984 - No. 24)
If (x - 2) and (x + 1) are factors of the expression x3 + px2 + qx + 1, what is the sum of p and q
9
-3
3
\(\frac{17}{3}\)
\(\frac{2}{3}\)
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
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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