Question

If x + 2 is a factor of x² + 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

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

and a + b = 4 ………….(1)

 

Solution :  

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.

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

HOPE THIS ANSWER WILL HELP YOU…

 

Some more questions :  

If the polynomial $f(x)=ax^{3}+bx-c$ is divisible by the polynomial $g(x)=x^{2}+bx+c$, then ab=

(a) 1

(b) $\frac{1}{c}$

(c) -1

(d) $-\frac{1}{c}$

https://brainly.in/question/7407444

 

If the polynomial $f(x)=ax^{3}+bx-c$ is divisible by the polynomial $g(x)=x^{2}+bx+c$,then c=

(a) b

(b) 2b

(c) $2b^{2}$

(d) -2b

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Answer 2

Step-by-step explanation:

given :-

• x + 2 is a factor of x² + ax + 2b .
• a + b = 4
• X = - 2

To find :-

• of x² + ax + 2b

Solution :-

put in eq

• (- 2)^2+ a (- 2) + 2b = 0
• 4 - 4a + 2b =0
• - 4a + 2b = - 4
• - 2 (2a-b) = - 4
• a - b = 2 .....eq1
• a + b = 4 ...eq2
• eq1 + 2
• 2a=6
• a = 3
• a + b = 4
• 3 + b = 4
• b = 1

Hence option b is correct answer .