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a) a=1,b=3 this is the answer
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p(x) = x² + ax + 2b
x + 2 is a factor of x² + ax + 2b ,
therefore,
p(x) = 0
p(-2) = 0
(-2)² + (-2)a + 2b = 0
4 - 2a + 2b = 0
2a - 2b = 4
a - b = 2 -------(i)
Given that, a + b = 4 , therefore
Adding eq(i) in a + b = 4, we get
a + b + a - b = 4 + 2
2a = 6
a = 3
Putting value of a in eq(i) ,
a - b = 2
3 - b = 2
b = 3 - 2
b= 1
Therefore, a = 3 and b = 1.
So, option (b) is the correct answer.
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