Playing with Vieta

Algebra Level 5

\[ \large x^4 + 37x^3 + 71x^2 + 18x + 3 \]

If \(a\), \(b\), \(c\), and \(d\) represent the roots of the polynomial above, find the sum of the coefficients of the monic polynomial whose roots are \( \large\frac{abc}{d}\), \(\large \frac{abd}{c}\), \(\large\frac{acd}{b}\), and \( \large\frac{bcd}{a}\).

Inspiration.

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