MathNet 2022-part-02 — 197 problems (EN–VI) Question 172

Let $a$, $b$, $c$, $d$ be roots of the equation $x^4 + x + 1 = 0$. Let $a^5 + 2a + 1$, $b^5 + 2b + 1$, $c^5 + 2c + 1$, $d^5 + 2d + 1$ be roots of the equation $x^4 + px^3 + qx^2 + rx + s = 0$. Find the value of $p + 2q + 4r + 8s$.