SOLUTION: If m and n are the roots of the equation {{{ ax^2+bx+c=0 }}} then what is the equation whose roots are {{{ m+(1/n) }}} and {{{ n+(1/m) }}} ?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: If m and n are the roots of the equation {{{ ax^2+bx+c=0 }}} then what is the equation whose roots are {{{ m+(1/n) }}} and {{{ n+(1/m) }}} ?      Log On


   

Question 630519: If m and n are the roots of the equation +ax%5E2%2Bbx%2Bc=0+ then what is the equation whose roots are +m%2B%281%2Fn%29+ and +n%2B%281%2Fm%29+ ?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
By Vieta's formulas, and .

Also, the quadratic that we want can be written in the form . Note that -d is the sum of the roots and e is the product of the roots. Add/multiply the two given roots, write in terms of a,b,c and you're done.