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Question
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x3 + 2ax2 + ax - 1
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Solution
Let p(x) x3 + 2ax2 + ax - 1 ...(i)
Since, (x - 2) is a factor of p(x), so p(2) = 0
Put x = 2 in equation (i), we get
p(2) = (2)3 - 2a(2)2 + a(2) -1
= 8 - 2a x 4 + 2a - 1
= 8 - 8a + 2a -1
= 7 - 6a
But p(2) = 0
7 - 6a = 0
⇒ -6a = -7
⇒ a = `(+7)/(+6)`
⇒ a = `(7)/(6)`.
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