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Question
If x + 2a is a factor of x5 – 4a2x3 + 2x + 2a + 3, find a.
Solution
According to the question,
Let p(x) = x5 – 4a2x3 + 2x + 2a + 3 and g(x) = x + 2a
g(x) = 0
⇒ x + 2a = 0
⇒ x = –2a
Therefore, zero of g(x) = –2a
We know that,
According to the factor theorem,
If g(x) is a factor of p(x), then p(–2a) = 0
So, substituting the value of x in p(x), we get,
p(–2a) = (–2a)5 – 4a2(–2a)3 + 2(–2a) + 2a + 3 = 0
⇒ –32a5 + 32a5 – 2a + 3 = 0
⇒ –2a = –3
⇒ a = `3/2`
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