Question

Two polynomials () =

3 + 3

2 − 13 and () = 2

3 − 5 +

when divided by + gives the same remainder. Find the value of .
​

Answer 1

Answer:

Given polynomial p(x)=ax  

3

+3x  

2

−13 and 2x  

2

−5x+a is divided by x-2 get same remainder

Then x-2=0 or x=2

p(x)=ax  

3

+3x  

2

−13

Replace x by 2 we get  

p(2)=a(2)  

3

+3(2)  

2

−13

⇒p(2)=8a+12−13

⇒p(2)=8a−1

2x  

2

−5x+a

Replace x by 2 we get

q(2)=2(2)  

3

−5(2)+a

⇒q(2)=16−10+a

⇒q(2)=6+a

Given remainder is same  

∴8a−1=6+a

⇒8a−1+1−a=6+a+1−a

⇒7a=7

a=1

Step-by-step explanation: