Roots to a Solution

Algebra Level 2

If $f(x) = x^3 + 2x^2 - 6x + 7$ , what is the sum of all $a^2$ for which $f(a)=0$ ?

1 solution

Oliver Papillo
May 17, 2017

Let the roots of $f(x)$ be $a$ , $b$ , and $c$ .

By Vieta's Formulas -

$\sum_{cyc}^{} a = -2$

$\sum_{cyc}^{} ab = -6$

and $abc = -7$

$\sum_{cyc}^{} a^2 = (\sum_{cyc} a)^2 - 2 * \sum_{cyc} ab$

$= 4 - 2* - 6$

$= 16$