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Question
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.
Options
– 6
6
7
– 7
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Solution
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is 7.
Explanation:
Let f(x) = 4x2 – kx + 5
When f(x) is divided by x – a then remainder = f(a)
Given f(x) is divided by x – 1 leaves a remainder 2
∴ f(1) = 2
`\implies` 4 × 12 – k + 5 = 2
`\implies` 4 – k + 5 = 2
`\implies` 9 – k = 2
`\implies` k = 9 – 2 = 7
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