Intersections of a line and a curve

[ehrenfest]

Homework Statement

For all all lines which meet the graph y = 2x^4+7x^3+3x-5 at four distinct points, what is the sum of the x-coordinates of the four points of intersection?

Homework Equations

The Attempt at a Solution

So, you obviously set ax+b =2x^4+7x^3+3x-5, but how do you find the zero's of that?

 

[Hurkyl]

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

 

[ehrenfest]

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

 

[Gib Z]

http://en.wikipedia.org/wiki/Viète's_formulas

Its a bit of grinding but in this case its a degree 4 polynomial so we can get it to the form $(x-\alpha)(x-\beta)(x-\gamma)(x-\delta)$. 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.