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Question
In the following two polynomials, find the value of ‘a’ if x – a is a factor of each of the two:
x5 - a2x3 + 2x + a + 1.
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Solution
Let p(x) = x5 - a2x3 + 2x + a + 1
Since (x -a) in a factor of p(x), so p(a) = 0.
Put x = a in equation (i) we get
p(a) = (a)5 - a2 (a)3 + 2a + a + 1 = 0
= a5 - a2 x a3 + 3a + 1 = 0
= a5 - a5 + 3a + 1 = 0
= 3a + 1 = 0
⇒ 3a = -1
⇒ a = `-(1)/(3)`.
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