Difference between revisions of "2019 AMC 12B Problems/Problem 21"
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==Problem== | ==Problem== | ||
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How many quadratic polynomials with real coefficients are there such that the set of roots equals the set of coefficients? (For clarification: If the polynomial is <math>ax^2+bx+c,a\neq 0,</math> and the roots are <math>r</math> and <math>s,</math> then the requirement is that <math>\{a,b,c\}=\{r,s\}</math>.) | How many quadratic polynomials with real coefficients are there such that the set of roots equals the set of coefficients? (For clarification: If the polynomial is <math>ax^2+bx+c,a\neq 0,</math> and the roots are <math>r</math> and <math>s,</math> then the requirement is that <math>\{a,b,c\}=\{r,s\}</math>.) | ||
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==See Also== | ==See Also== | ||
{{AMC12 box|year=2019|ab=B|num-b=20|num-a=22}} | {{AMC12 box|year=2019|ab=B|num-b=20|num-a=22}} | ||
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Revision as of 17:48, 14 February 2019
Problem
How many quadratic polynomials with real coefficients are there such that the set of roots equals the set of coefficients? (For clarification: If the polynomial is 
and the roots are 
and 
then the requirement is that 
.)
Solution
See Also
| 2019 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 20 |
Followed by Problem 22 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
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