Question

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

Options

• a= 1, b = 3

• a = 3, b = 1

• a = −1, b = 5

• a = 5, b = −1

Answer 1

Given that x + 2 is a factor of `x^2 + ax + 2b` and a + b=4

`f(x)=x  ^2 +ax + 2b`

`f(-2)= (-2)^2 +a(-2 )+ 2b`

`0 = 4-2a +2b`

`-4 = -2a+2b`

By solving `-4 = -2a+2b` and a + b = 4 by elimination method we get 

Multiply `a+b =4`by  2 we get,

`4 = 4b`

`4/4=b`

By substituting b = 1 in a + b = 4 we get

`a+1 =4`

`a = 4-1`

`a =3`

Then a = 3, b = 1

Hence, the correct choice is `(b).`