Question

5.
Determine the value of 'a', if (x - a) is a factor of the polynomial x? - (a? - 1)x+2.​

Answer 1

Answer:

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:

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