Question 1 Report
If (x - 2) and (x + 1) are factors of the expression x3 + px2 + qx + 1, what is the sum of p and q
Answer Details
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 = −32 − 3 2 q = −32 − 3 2 p + q = 32 3 2 - 32 3 2 = −62 − 6 2 = -3
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