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) }}} ?

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) }}} ?

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Question 630519: If m and n are the roots of the equation then what is the equation whose roots are and ?
Answer by richard1234(7193) (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.
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