Question

If the polynomials ax 3 +5x²-14
and 3x3 – 7+a are by
(x-1) leave the same reminder
value of a.
find
​

Answer 1

Answer:

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Step-by-step explanation:

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