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Question
Find the value of a and b so that the polynomial x3 - ax2 - 13x + b has (x - 1) (x + 3) as factor.
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Solution
Let p(x) = x3 - ax2 - 13x + b be the given polynomial.
If (x - 1) and (x + 3) are the factors of p(x) then
p(1) = 0
and p(-3) = 0
p(1) = (1)3 - a(1)2 - 13(1) + b = 0
= 1 - a - 13 + b = 0
a - b = -12 ...(1)
p(-3) = (-3)3 - a(-3)2 - 13(-3) + b = 0
= -27 - 9a + 39 + b = 0
9a - b = 12 ...(2)
Solving (1) and (2) we get
a = 3
and b = 15.
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