Kyuubi-c?-2

Algebra Level 4

Let $f(x)=ax^3+bx^2+cx+d$ with real numbers $a,b,c,d$ satisfying $|f(1)|=|f(2)|=|f(3)|=|f(4)|=|f(5)|=|f(6)|=|f(7)|=12$ .

Find $|f(0)|$ .

Notation : $| \cdot |$ denotes the absolute value function .

1 solution

Ishan Singh
May 30, 2016

Let $g(x) = f(x) \pm12$

Note that from the given conditions, $g(x)$ is at most degree $3$ , but has at least $4$ roots (by PHP). Hence it is an identity.

$\implies g(0) = 0$

$\therefore |f(0)| = \boxed{12}$

$f(0)$ could be $-12$

Otto Bretscher - 5 years ago

Small typo, corrected.

Ishan Singh - 5 years ago

Nice solution

Mardokay Mosazghi - 5 years ago