1965 AHSME Problems/Problem 7
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
=>
.