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Question
If both (x − 2) and `(x - 1/2)` is the factors of ax2 + 5x + b, then show that a = b
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Solution
p(x) = ax2 + 5x + b
when (x − 2) is a factor
P(2) = 0
a(2)2 + 5(2) + b = 0
4a + 10 + b = 0
4a + b = −10 ...(1)
when `(x - 1/2)` is a factor
`"p"(1/2)` = 0
`"a"(1/2)^2 + 5(1/2) + "b"` = 0
Multiply by 4
a + 10 + 4b = 0
a + 46 = −10 ...(2)
From (1) and (2) we get
4a + b = a + 4b
4a – a = 4b – b
3a = 3b
a = b
Hence it is proved.
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