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Intersections of a line and a curve 
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#1
Jul2107, 09:40 PM

P: 1,996

1. The problem statement, all variables and given/known data
For all all lines which meet the graph y = 2x^4+7x^3+3x5 at four distinct points, what is the sum of the xcoordinates of the four points of intersection? 2. Relevant equations 3. The attempt at a solution So, you obviously set ax+b =2x^4+7x^3+3x5, but how do you find the zero's of that? 


#2
Jul2107, 09:47 PM

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You don't need to know the roots; you only need to know their sum.



#3
Jul2207, 12:35 AM

P: 1,996

Yes and how do you know their sum without knowing the roots?



#4
Jul2207, 03:35 AM

HW Helper
P: 3,352

Intersections of a line and a curve
http://en.wikipedia.org/wiki/Vi%C3%A8te%27s_formulas
Its a bit of grinding but in this case its a degree 4 polynomial so we can get it to the form [itex](x\alpha)(x\beta)(x\gamma)(x\delta)[/itex]. Where the greek letters are the roots. Now expand that, and equate to co efficients and we can get an expression for the sum of the roots knowing only the coefficients. 


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