How hard can this be?

Algebra Level pending

Let $f(x)$ be a 5th degree polynomial of the form ${ x }^{ 5 }+a{ x }^{ 4 }+{ bx }^{ 3 }+c{ x }^{ 2 }+dx+e$ .

Also, $f(n)=10n$ for $n = 1, 2, 3, 4, 5$ .

Find $a+b+c+d+e.$

1 solution

Julian Yu
Oct 20, 2015

$f(1) = 1+a+b+c+d+e$

From the second condition, $f(1) = 10$

Therefore, $1+a+b+c+d+e = 10$

$a+b+c+d+e=\boxed { 9 }$