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Question
In the following two polynomials, find the value of a, if x + a is a factor x4 − a2x2 + 3x −a.
Solution
Let `f(x) = x^4 - a^2x^2 + 3x - a ` be the polynomial. By factor theorem, (x + a) is a factor of the f(x), if f(− a) = 0, i.e.,
`f(-a) = (-a)^4 - a^2 (-a)^2 + 3(-a)-a = 0`
`a^4 - a^4 - 3a - a = 0`
-4a = 0
`a = 0`
Thus, the value of a is 0.
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