Question

find the value of a if x-a is a factor of the polynomial x cube +ax square -2x+a+4​

Answer 1

Answer:

Let

P(x)=x  

2

+ax+b

Q(x)=x  

2

+bx+a

Given that P(x) and Q(x) have a common factor.

Let (x−α) be the common factor.

Therefore,

α  

2

+aα+b=0.....(1)

α  

2

+bα+a=0.....(2)

Subtracting eq  

n

(1) from (2), we have

(α  

2

+aα+b)−(α  

2

+bα+a)=0

α  

2

+aα+b−α  

2

−bα−a=0

(a−b)α−(a−b)=0

(a−b)(α−1)=0

⇒α=1

Substituting the value of α in eq  

n

(1), we have

(1)  

2

+a(1)+b=0

⇒a+b+1=0

Hence the correct answer is (B)a+b+1=0

Step-by-step explanation: