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!

Quaratic Equations

  1. Jul 9, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex] |ax^{2}+bx+c|\leq1 \forall x\in[0,1][/tex]
    Find the maximum magnitude of a,b, and c possible!

    My attempt:
    putting x=0;
    hence its maximummagnitude is 1.
    Help me with a and b.
  2. jcsd
  3. Jul 9, 2008 #2


    User Avatar
    Homework Helper

    You aren't going to be able to set limits on the coefficients separately, I think. You are probably going to have relationships between the coefficients.

    Picture it this way. The inequality is saying that

    -1 \leq ax^{2}+bx+c \leq 1[/tex] for [tex] 0 \leq x \leq 1[/tex].

    So a portion of the curve for this function has to fit entirely in the "box" bounded by x = 0, x = 1, y = -1, and y = 1. (Obviously, the parabola goes on forever elsewhere...) What does that mean for intersection points of the parabola with the "box"? How might you find coefficients from that?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Quaratic Equations
  1. Quadratic Equation (Replies: 6)

  2. Trig equation (Replies: 10)

  3. Equation query (Replies: 4)

  4. Solving an equation (Replies: 4)