Better Students Ask More Questions.
What is a if the 1/m+1/n=1/5? m,n are roots of equation x^2-x-a=0
1 Answer | add yours
You need to bring the summation `1/m + 1/n` to a common denominator, such that:
`1/m + 1/n = (m + n)/(mn)`
Replacing `(m + n)/(mn)` for `1/m + 1/n` in equation `1/m + 1/n = 1/5` , yields:
`(m + n)/(mn) = 1/5`
Since the problem provides the information that m and n are the solution to the quadratic equation `x^2 - x - a = 0` , you need to use Vieta's formulas, such that:
`m + n = -(-1)/1 => m + n = 1`
`m*n = -a/1 => m*n = -a`
Replacing 1 for m + n and -a for m*n in equation `(m + n)/(mn) = 1/5` yields:
`1/(-a) = 1/5 => a = -5`
Hence, evaluating the value of coefficient `a` , using Vieta's formulas, under the given conditions, yields `a = -5.`
Posted by sciencesolve on October 3, 2013 at 5:21 PM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.