Difference between revisions of "1965 AHSME Problems/Problem 7"
Tecilis459 (talk | contribs) m (Fix answer regarding statement) |
(see also box) |
||
| Line 16: | Line 16: | ||
Applying the formulas, we get <math>\frac{\frac{-b}{a}}{\frac{c}{a}}</math>, or <math>\frac {-b}{c}</math> => <math>\boxed{E}</math>. | Applying the formulas, we get <math>\frac{\frac{-b}{a}}{\frac{c}{a}}</math>, or <math>\frac {-b}{c}</math> => <math>\boxed{E}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AHSME 40p box|year=1965|num-b=6|num-a=8}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
Revision as of 08:57, 18 July 2024
Problem
The sum of the reciprocals of the roots of the equation 
is:
Solution
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 
=> 
.
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 | ||
