Difference between revisions of "1965 AHSME Problems/Problem 7"
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Latest revision as of 16:04, 18 July 2024
Contents
Problem
The sum of the reciprocals of the roots of the equation 
is:
Solution 1
Using Vieta's formulas, we can write the sum of the roots of any quadratic equation in the form 
as 
, and the product as 
.
If 
and 
are the roots, then the sum of the reciprocals of the roots is 
.
Applying the formulas, we get 
, or 
=> 
.
Solution 2
Let 
. 
has roots and , and so 
has roots 
and 
. Because 
, by Vieta's formulas, 
, which is answer choice 
.
See Also
| 1965 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
