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Question
One factor of x3 – kx2 + 11x – 6 is x – 1. The value of k is ______.
Options
– 6
12
6
–12
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Solution
One factor of x3 – kx2 + 11x – 6 is x – 1. The value of k is 6.
Explanation:
Let f(x) = x3 – kx2 + 11x – 6
Since x – 1 is a factor of f(x)
∴ f(1) = 0
`\implies` 13 – k · 12 + 11 – 6 = 0
`\implies` 1 – k + 11 – 6 = 0
`\implies` 6 – k = 0
`\implies` k = 6
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