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Question
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1).
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Solution
Let f(x) = (3k + 2)x3 + (k − 1)
2x + 1 = 0
`\implies x = (−1)/2`
Since, 2x + 1 is a factor of f(x), remainder is 0.
∴ `(3k + 2)((-1)/2)^3 + (k - 1) = 0`
`\implies (3k + 2)((-1)/8) + (k - 1) = 0`
`\implies (-(3k + 2))/8 + (k - 1) = 0`
`\implies (-3k - 2 + 8k - 8)/ 8 = 0`
⇒ (−3k − 2 + 8k − 8) = 0 × 8
⇒ 5k – 10 = 0
⇒ 5k = 10
⇒ k = `10/5`
⇒ k = 2
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