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Homework Help: Online assignments = confusion!

  1. Mar 5, 2009 #1
    I'm doing an online course, and am finding it to be extremely difficult to do without having an actual teacher that you can sit with and a classroom full of others you can work with.

    1. One of the questions is:
    Determine a general equation for the quartic function f(x) as described:
    f(x)<0 when x< -2, f(x)>0 when -2<x<3, and f(x)<0 when x>3, the zeros are -2, -1, and 3.

    I've never worked with quartic functions or anything like this.
    If anyone has some guidance that would be fantastic!!!
     
  2. jcsd
  3. Mar 5, 2009 #2

    Mentallic

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    Homework Helper

    It's not much more than just an extension from quadratics/cubics.
    The general form is [tex]y=ax^4+bx^3+cx^2+dx+e[/tex] but this wont help much in this case.
    Using the fact that for a quartic in the form [tex]y=a(x-b)(x-c)(x-d)(x-e)[/tex], the roots are [tex]b, c, d, e[/tex] so since you know the roots are -2,-1 and 3, It can be written as [tex]y=(ax+b)(x+2)(x+1)(x-3)[/tex]
    Now just see if you can add anything from the other info given. Such as finding whether a is positive or negative (the coefficient of the highest power ([tex]x^4[/tex]) is important such as how it makes quadratics concave up or concave down).
     
  4. Mar 6, 2009 #3

    HallsofIvy

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    Because "f(x)>0 when -2<x<3", the graph of f does not cross the x axis at x= -1. But x= -1 is a zero so the graph must be tangent to the axis there. That means x= -1 is a double root" the four[/b roots are -2, -1, -1, 3, and so gives you the fourth factor that Mentallic writes as "ax+ b".
     
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