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Question
If x + 1 is a factor of ax3 + x2 – 2x + 4a – 9, find the value of a.
Solution
Let p(x) = ax3 + x2 – 2x + 4a – 9
Since, x + 1 is a factor of p(x), then put p(–1) = 0
∴ a(–1)3 + (–1)2 – 2(–1) + 4a – 9 = 0
⇒ –a + 1 + 2 + 4a – 9 = 0
⇒ 3a – 6 = 0
⇒ 3a = 6
⇒ `a = 6/3 = 2`
Hence, the value of a is 2.
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