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1981 AMC 12 Question 30

AMC12 · 1981 AMC 12

Question 30

If $a,$ $b,$ $c,$ $d$ are the solutions of the equation $x^4-bx-3=0,$ then an equation whose solutions are $$
\begin{gathered} \frac{a+b+c}{d^2},\quad \frac{a+b+d}{c^2},\\ \frac{a+c+d}{b^2},\quad \frac{b+c+d}{a^2} \end{gathered}
$$ is
  1. $3x^4+bx+1=0$
  2. $3x^4-bx+1=0$
  3. $3x^4+bx^3-1=0$
  4. $3x^4-bx^3-1=0$
  5. none of these