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Question
If x − 2 is a factor of the following two polynomials, find the values of a in each case x3 − 2ax2 + ax − 1.
Solution
Let `f(x) = x^3 - 2ax^2 + ax - 1` be the given polynomial.
By factor theorem, if (x − 2) is a factor of f(x), then f (2) = 0
Therefore,
`f(2) = (2)^3 - 2a(2)^2 a(2) - 1 = 0`
`8-8a + 2a - 1 = 0`
`-6a + 7 = 0`
`a = 7/6`
Thus the value of a is 7/6.
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