Question

The polynomial (x − a), where a > 0, is a factor of the polynomial q x( ) 4 2 x 2– = 2 . Which of these is a polynomial whose factor is x a 1 c m – ?

Answer 1

Answer:

Let functions f(x) and g(x) be polynomials such that g(x) is factor of f(x).

Then the root of g(x) will be also the root of f(x).

So, as per the question (x−a) is a factor of x

6

−ax

5

+x

4

−ax

3

+3x−a+2=0

Root of x−a is a.

Therefore a is also the root of x

6

−ax

5

+x

4

−ax

3

+3x−a+2=0.

putting x=a

⇒a

6

−aa

5

+a

4

−aa

3

+3a−a+2=0

⇒a

6

−a

6

+a

4

−a

4

+2a+2=0

⇒2a+2=0

⇒a=−1

So, the value of a is −1.

Step-by-step explanation:

This is your answer and explanation