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Question
If (x – a) is a factor of x3 – ax2 + x + 5; the value of a is ______.
Options
`1/5`
5
`-1/5`
–5
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Solution
If (x – a) is a factor of x3 – ax2 + x + 5; the value of a is –5.
Explanation:
Let f(x) = x3 – ax2 + x + 5
Since x – a is a factor of f(x)
∴ f(a) = 0
`\implies` a3 – a · a2 + a + 5 = 0
`\implies` a3 – a3 + a + 5 = 0
`\implies` a + 5 = 0
`\implies` a = –5
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