Question

P(x) is a polynominal satisfying $P(x+\frac{3}{2})=P\left(x\right)$, for all real values of x. If P(5) = 2002, then P(8) equals ..

• A. 2002
• B. 2003 $\frac{1}{2}$
• C. $\frac{2003}{2}$
• D. 2002 $\frac{1}{2}$

Answer 1

The correct option is A 2002

if $p\left(x\right)=p(x+\frac{3}{2})$
then consider $x=5$
so
$p\left(5\right)=p(5+\frac{3}{2})$
now consider $x=5+\frac{3}{2}$
so according to relation $p\left(x\right)=p(x+\frac{3}{2})$ , $p(5+\frac{3}{2})=p(5+\frac{3}{2}+\frac{3}{2})=p(5+3)=p\left(8\right)$
so by this relation we conclude that $p\left(5\right)=p\left(8\right)$
as $p\left(5\right)=2002$
then also $p\left(8\right)=2002$