Question

please answer my question ​

Answer 1

Let p(x)=x  

3

+2x  

2

−5ax−7

and q(x)=x  

3

+ax  

2

−12x+6 be the given polynomials,

Now, R  

1

​

= Remainder when p(x) is divided by x+1.

⇒R  

1

​

=p(−1)

⇒R  

1

​

=(−1)  

3

+2(−1)  

2

−5a(−1)−7[∵p(x)=x  

2

+2x  

2

−5ax−7]

⇒R  

1

​

=−1+2+5a−7

⇒R  

1

​

=5a−6

And R  

2

​

= Remainder when q(x) is divided by x-2

⇒R  

1

​

=q(2)

⇒R  

2

​

=(2)  

3

+a×2  

2

−12×2+6[∵q(x)=x  

2

+ax  

2

−12x−6]

⇒R  

2

​

=8+4a−24+6

⇒R  

2

​

=4a−10

Substituting the values of R  

1

​

 and R  

2

​

 in 2R  

1

​

+R  

2

​

=6, we get

⇒2(5a−6)+(4a−10)=6

⇒10a−12+4a−10=6

⇒14a−22=6

⇒14a−28=0

⇒a=2