Marinada '21

[lang=hr] Zadan je polinom $P(x) = x^3 - 7x^2 + 10x + a$ koji ima nultočke $x_1$, $x_2$ i $x_3$. Odredite vrijednost parametra $a$ tako da je izraz $| x_1^5 + x_2^5 + x_3^5 |$ minimiziran. Moguće je pokazati da se odgovor može napisati u obliku $\frac{n}{m}$ za prirodne brojeve $n$ i $m$. [/lang] [lang=en] The polynomial $P(x) = x^3 - 7x^2 + 10x + a$ is given. It's roots are $x_1$, $x_2$ and $x_3$. Determine the value of the parameter $a$ such that the expression $| x_1^5 + x_2^5 + x_3^5 |$ is minimized. It can be shown that the answer has the form of $\frac{n}{m}$ for positive integers $n$ and $m$. [/lang]