1. The problem statement, all variables and given/known data 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? 2. Relevant equations 3. 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?
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 [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.