Question

If x+ 2 is a factor of $x^{2}+ax+2b$ and a+b=4, then
(a) a=1,b=3
(b) a=3,b=1
(c) a=-1,b=5
(d) a=5,b=-1

Answer 1

SOLUTION :  

The correct option is (b) : a = 3 and b = 1 .

Given : (x + 2) is a factor of f(x) : x² + ax + 2b  

and a + b = 4 ………….(1)

Let g(x) = x +2

For the zero of g(x) = x +2, put g(x) = 0

Therefore, x +2 = 0  

x = -2  

On putting x = -2 in f(x),

f(x) = x² + ax + 2b  

f(-2) = (-2)² + a(-2) + 2b

= 4 -2a + 2b  

-4 = -2a + 2b  

- 4 = -2(a - b)

-4/-2 = a - b  

2 = a - b  

a - b = 2 …………… (2)

On adding eq 1 & 2,  

a + b = 4  

a - b = 2

--------------

2a = 6

a = 6/2 = 3  

a = 3

On putting a = 3 in eq 1,

a + b = 4  

3 + b = 4

b = 4 - 3

b = 1

Hence, the value of a is 3 and b is 1.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Heya mate,
Here's your answer
=> it's here in the attachment (b Is correct)
Hope it helps you!
Plz mark my answer as branliest ❤️☺️