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1950 AMC 12 Question 38

AMC12 · 1950 AMC 12

Question 38

If the expression $$
\begin{vmatrix}a&c\\d&b\end{vmatrix}
$$ has the value $ab-cd$ for all values of $a,$ $b,$ $c,$ and $d,$ then the equation $$
\begin{vmatrix}2x&1\\x&x\end{vmatrix}=3
$$
  1. Is satisfied for only $1$ value of $x$
  2. Is satisfied for $2$ values of $x$
  3. Is satisfied for no values of $x$
  4. Is satisfied for an infinite number of values of $x$
  5. None of these