2022 AMC 10B Problems/Problem 7: Difference between revisions
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<math>p+q=-k</math> | <math>p+q=-k</math> | ||
<math>p*q=36</math> | <math>p*q=36</math> | ||
(Let <math>p</math> and <math>q</math> be the roots) | (Let <math>p</math> and <math>q</math> be the roots) | ||
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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= | Thus, we have a total of <math>4</math> pairs and another <math>4</math> pairs (the negatives), which total us <math>4+4=\boxed{\textbf{(B) }8}</math>. | ||
Revision as of 15:27, 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 
.
