Grade 9Algebra

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)?

Vishal Venkat

9 Years agoGrade 9

1 Answer

Arun

9 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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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)?

Vishal Venkat

1 Answer

Arun

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