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Question
If (3x – 2) is a factor of 3x3 – kx2 + 21x – 10, find the value of k.
Solution
Let 3x – 2 = 0,
then 3x = 2
⇒ x = `(2)/(3)`
Substituting the value of x in f(x),
f(x) = 3x3 – kx2 + 21x – 10
`f(2/3) = 3(2/3)^3 - k(2/3)^2 + 21(2/3) - 10`
= `3 xx (8)/(27) - k xx (4)/(9) + 21 xx (2)/(3) - 10`
= `(8)/(9) - (4k)/(9) + 14 - 10`
= `(8 - 4k)/(9) + 4`
∵ Remainder is 0
`(8 - 4k)/(9) + 4` = 0
⇒ 8 – 4k + 36 = 0
⇒ –4k + 44 = 0
⇒ 4k = 44
∴ k = 11.
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