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Question
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
Options
a= 1, b = 3
a = 3, b = 1
a = −1, b = 5
a = 5, b = −1
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Solution
Given that x + 2 is a factor of `x^2 + ax + 2b` and a + b=4
`f(x)=x ^2 +ax + 2b`
`f(-2)= (-2)^2 +a(-2 )+ 2b`
`0 = 4-2a +2b`
`-4 = -2a+2b`
By solving `-4 = -2a+2b` and a + b = 4 by elimination method we get
Multiply `a+b =4`by 2 we get,
`4 = 4b`
`4/4=b`
By substituting b = 1 in a + b = 4 we get
`a+1 =4`
`a = 4-1`
`a =3`
Then a = 3, b = 1
Hence, the correct choice is `(b).`
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