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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:
x2 - 3x + 5a
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Solution
Let p(x) = x2 - 3x + 5a ...(i)
Since, (x - 2) is a factor of p(x), so p(2) = 0 ...(by factor theorem)
Put x = 2 in equation (i), we get
p(2) = (2)2 - 3 x 2 + 5a
= 4 - 6 + 5a
= 5a - 2
But p(2) = 0
⇒ 5a -2 = 0
⇒ 5a = 2
⇒ a = `(2)/(5)`.
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