Fun with Monics 1

Algebra Level 4

$P(x)$ is a monic polynomial.

And

$y=P(x)$ and

$y=2x+1$ . Meet at

$x=1,2,3,4$

Find $P(0)$

Given that $P(x)$ is a polynomial of degree $\boxed{\boxed{4}}$

2 solutions

Rushikesh Joshi
Jan 22, 2015

Pranjal Jain
Jan 22, 2015

Consider $g(x)=P(x)-(2x+1)$ .

Clearly, $g(x)$ is monic polynomial of degree 4 and it has roots $x=1,2,3,4$ .

$g(x)=(x-1)(x-2)(x-3)(x-4)$ $\Rightarrow P(x)=(x-1)(x-2)(x-3)(x-4)+(2x+1)$ $P(0)=4!+1=25$

@Parth Lohomi This is overrated!!

Pranjal Jain - 6 years, 4 months ago