Question

1. The polynomial ax + 3x2 - 13 and 2x - 5x + a leave the same remainder in each case, when divided
by (x - 2). Find the value of a.
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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

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Answer 2

Answer:

: 1

Step-by-step explanation: