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Question
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
Options
8
3
– 5
– 8
Solution
If x – 3 is a factor of x2 + kx + 15; the value of k is – 8.
Explanation:
Let f(x) = x2 + kx + 15
Given x – 3 is a factor of f(x)
∴ f(3) = 0
`\implies` 32 + k × 3 + 15 = 0
`\implies` 9 + 3k + 15 = 0
`\implies` 3k + 24 = 0
`\implies` 3k = – 24
`\implies` k = – 8
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