Question

p(x) is a polynomial satisfying p(x+(3/2))=p(x) for all real values of x. If p(5)=2010,what is the value of p(8)?

Answer 1

p (x+(3/2))=p (x)

put x=5

p (5+3/2)=p (5)

p (13/2)=p (5)

but we have given p (5)=2010

so,
p(13/2)=p (5)=2010

now,

put x=13/2

p (13/2+3/2)=p (13/2)

p (8)=p (13/2)

because p (13/2)=2010

so, p (8)=p (13/2)=2010

hence,
p (8)=2010

Answer 2

Answer:

2010

Step-by-step explanation:

given,

p(x+3/2)=p(X )

Then

p(5+3/2)=p(13/2) =p(5)=2010(given)

p(13/2+3/2)=p(8)=p(13/2)

=2010