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p(x) is a monic polynomial of degree 2016.If p(0)=2015,p(1)=2014,p(2)=2013,...,p(2015)=0,what is the value of p(2016)?

p(x) is a monic polynomial of degree 2016.If p(0)=2015,p(1)=2014,p(2)=2013,...,p(2015)=0,what is the value of p(2016)?

Grade:9

1 Answers

Arun
25750 Points
6 years ago
because p(x) is monic polynomial hence let
p(x) = ax+b  where a,b are constants
now p(0)= 2015       given
hence 2015= a*0 + b
so b = 2015
now p(1)= 2014       given
hence 2014= a*1 +b
2014= a+ 2015          (as we have already found out b)
so a= –1
 
now P(x) = –x+ 2015
so P(2016) = –2016+2015
P(2016)= –1
 
Note-  only any two conditions are sufficient because there are two variables a, b. you can choose any two conditions.
hope it helps

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