I'm not quite sure what you mean by "r and s are the roots of..."
Do you mean that r and s are the two values for x in this equation?
This is how I'll solve it. If I misinterpreted the question let me know.
2x2 -5x -7 =0
Let's factor the polynomial and then find the values of x.
(2x+7)(x-1) = 0
------
(2x+7) = 0
2x = -7
x = -3½
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(x-1) = 0
x = 1
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So let's say r = 3½ and s = 1
Let's put this in the equation.
r/s + s/r
3.5/1 + 1/3.5
12.25/3.5 + 1/3.5
13.25/3.5
Well...that would be the answer.
Sorry if I totally bombed this, I think the problem was that I didn't really understand the question.
