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Q.

If x + 2 is a factor of x2+ax+2b=0 and a+b=4, then


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a

 a=1,b=3

b

 a=3,b=1

c

 a=-1,b=5

d

 a=5,b=-1 

answer is B.

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Detailed Solution

Given that x+2 is a factor of x2+ax+2b 
So,
(x+2)=0
x=-2
Put x=-2, in given polynomial,
fx=x2+ax+2b
f(-2)=(-2)2+a(-2)+2b
f-2=4-2a+2b
4-2a+2b=0
2b=2a-4
b=a-2……………….1
Given,
a+b=4
a+a-2=4         (from equation 1)
2a=4+2 a=62
a=3
Thus,
b=3-2      (from equation 1)
b=1
So, the obtained values are a = 3 and b = 1.
Therefore, option 2 is the correct.
 
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