# If x + 2 is a factor of x2 + ax + 2b and a + b = 4, thenA. a = 1,b = 3B. a = 3,b = 1C. a = – 1,b = 5D. a = 5,b = – 1

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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