2022 AMC 10B Problems/Problem 7

Revision as of 15:26, 17 November 2022 by Stevens0209 (talk | contribs)

Using Vieta's Formula, this states:

$p+q=-k$ $p*q=36$ (Let $p$ and $q$ be the roots)

This shows that p and q must be the factors of $36$: $1, 36, 2, 18, 3, 12, 4, 9, 6$ and its negative counterpart.

We cancel out the $6$ and $6$ because the problem states that it wants distinct roots.

Thus, we have a total of $4$ pairs and another $4$ pairs (the negatives), which total us $4+4=8$. $\boxed{\textbf{(B) }8\boxed$ (Error compiling LaTeX. Unknown error_msg).