2022 AMC 10B Problems/Problem 7: Difference between revisions
Stevens0209 (talk | contribs) Created page with "Using Vieta's Formula, this states: <math>p+q=-k</math> <math>p*q=36</math> (Let <math>p</math> and <math>q</math> be the roots) This shows that p and q must be the factors..." |
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This shows that p and q must be the factors of <math>36</math>: <math>1, 36, 2, 18, 3, 12, 4, 9, 6</math> and its negative counterpart. | This shows that p and q must be the factors of <math>36</math>: <math>1, 36, 2, 18, 3, 12, 4, 9, 6</math> and its negative counterpart. | ||
We cancel out the <math>6</math> and <math>6</math> because the problem states that it wants distinct roots. | We cancel out the <math>6</math> and <math>6</math> because the problem states that it wants distinct roots. | ||
Thus, we have a total of <math>4</math> pairs and another <math>4</math> pairs (the negatives), which total us <math>4+4=8</math>. | Thus, we have a total of <math>4</math> pairs and another <math>4</math> pairs (the negatives), which total us <math>4+4=8</math>. | ||
<math>\boxed{\textbf{(B) }8</math>. | <math>\boxed{\textbf{(B) }8\boxed</math>. | ||
Revision as of 15:26, 17 November 2022
Using Vieta's Formula, this states:
(Let 
and 
be the roots)
This shows that p and q must be the factors of 
: 
and its negative counterpart.
We cancel out the 
and because the problem states that it wants distinct roots.
Thus, we have a total of 
pairs and another pairs (the negatives), which total us 
.
$\boxed{\textbf{(B) }8\boxed$ (Error compiling LaTeX. Unknown error_msg).
