Question

Consider a polynomial of degree $4$ with leading coefficient $2$ such that $P\left(1\right)=1,P\left(2\right)=16,P\left(3\right)=81,P\left(4\right)=256$ then $P\left(5\right)$ is :

• A. $673$
• B. $637$
• C. $727$
• D. $Noneofthese$

Answer 1

The correct option is A $673$

$p\left(x\right)=2(x-1)(x-2)(x-3)(x-4)+x^4$

On putting x=1

P(1)=1 Which satisfies the cond?

Similarly, $P\left(2\right)=16,P\left(3\right)=81,P\left(4\right)=256$

Put $x=5$

$P\left(5\right)=2\times 4\times 3\times 2\times 1+(5{)}^4$

$=48+625$

$P\left(5\right)=673$