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