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1965 AMC 12 Question 22

AMC12 · 1965 AMC 12

Question 22

If $a_2\ne0$ and $r,$ $s$ are the roots of $a_0+a_1x+a_2x^2=0,$ then the equality

$$
\begin{aligned} a_0+a_1x+a_2x^2 &=a_0\left(1-\frac xr\right)\\ &\quad\cdot\left(1-\frac xs\right) \end{aligned}
$$

holds:
  1. for all values of $x,$ $a_0\ne0$
  2. for all values of $x$
  3. only when $x=0$
  4. only when $x=r$ or $x=s$
  5. only when $x=r$ or $x=s,$ $a_0\ne0$