1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Intersections of a line and a curve

  1. Jul 21, 2007 #1
    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?
    Last edited: Jul 21, 2007
  2. jcsd
  3. Jul 21, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You don't need to know the roots; you only need to know their sum.
  4. Jul 22, 2007 #3
    Yes and how do you know their sum without knowing the roots?
  5. Jul 22, 2007 #4

    Gib Z

    User Avatar
    Homework Helper


    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Intersections of a line and a curve
  1. Intersection of Lines (Replies: 5)