I. $2x^2 + 9x - 45 = 0$ II. $4y^2 + 19y + 22 = 0$ What is the relation between $x$ and $y$?

If $x > y$
If $x = y$ or the relation cannot be established
If $x < y$
If $x \le y$

Correct answer: If $x = y$ or the relation cannot be established

Solution

Solve the quadratics by factoring. The first gives roots $x=\frac{15}{2}$ and $x=-3$, while the second gives roots $y=-2$ and $y=-\frac{11}{4}$. Since different valid pairs give different relations, a definite comparison is not possible.

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