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

Given;


A factor = x + 2


So,


x + 2 = 0


x = – 2


p(x) = x2 + ax + 2b


p( – 2) = ( – 2)2 + ( – 2)a + 2b


0 = 4 – 2a + 2b


– 4 = – 2 (a – b)


2 = a – b……………Equation (i)


4 = a + b …….. Equation (ii)


By Adding (i) and (ii) we get,


2 – a + b + 4 – a – b = – 2a + 2


2a = 2


So we get, a = 3 and b = 1

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