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Question
If (x + a) is a factor of `(2x^2 + 2ax + 5x + 10)`, then find the value of a.
Solution
Given: (x + a) is a factor of `2x^2 + 2ax + 5x + 10`
We have
x + a = 0
⇒ x = –a
Since, (x + a) is a factor of `2x^2 + 2ax + 5x + 10`
Hence, It will satisfy the above polynomial
∴ `2(–a)^2 + 2a(–a) + 5(–a) + 10 = 0`
`⇒ –5a + 10 = 0`
`⇒ a = 2`
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