SOLUTION: If the sum of the reciprocals of the roots of the equation 3x^2+7x+k is-7/3,what is k? Thank you.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If the sum of the reciprocals of the roots of the equation 3x^2+7x+k is-7/3,what is k? Thank you.      Log On


   

Question 1068462: If the sum of the reciprocals of the roots of the equation 3x^2+7x+k is-7/3,what is k? Thank you.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%283x-a%29%28x-b%29=3x%5E2%2B7x%2Bk
3x%5E2-3bx-ax%2Bab=3x%5E2%2B7x%2Bk
3x%5E2-%283b%2Ba%29x%2Bab=3x%5E2%2B7x%2Bk
So,
3b%2Ba=-7
and
ab=k
and
3%2Fa%2B1%2Fb=-7%2F3
Multiply both sides by ab,
3b%2Ba=-%287%2F3%29%28ab%29
Comparing to the previous equations,
-7=-%287%2F3%29k
k=3