Question

Let $P\left(x\right)$ is polynomial of degree $4$ such that $P\left(1\right)=2,P\left(2\right)=5,P\left(3\right)=10$ and $P\left(4\right)=17$ then $P\left(5\right)=$......

• A. $26$
• B. $50$
• C. $35$
• D. $60$

Answer 1

The correct option is B $50$

If $P\left(x\right)$ is polynomial of degree $4$ such that,

$P\left(1\right)=2,P\left(2\right)=5,P\left(3\right)=10$ and $P\left(4\right)=17$ then,

The required polynomial is $P\left(x\right)=(x-1)(x-2)(x-3)(x-4)+x^2+1$

Now $P\left(5\right)=(5-1)(5-2)(5-3)(5-4)+5^2+1$

$⟹P\left(5\right)=4\times 3\times 2\times 1+25+1$

$⟹P\left(5\right)=24+26$

$\therefore P\left(5\right)=50$