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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:
x6 - ax5 + x4 - ax3 + 3a + 2
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Solution
Let p(x) = x6 - ax5 + x4 - ax3 + 3a + 2 ...(i)
Put x = a in equation (i) we get
p(a) = (a)6 - a(a)5 + (a)4 - a(a)3 + 3(a) + 2
= a6 - a6 + a4 - a4 + 3a + 2 = 0
∴ 3a = -2
∴ a = `(-2)/(3)`.
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