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Homework Help: Quadratic functions

  1. Feb 12, 2007 #1
    1. A quadratic fraction is of the form f(x)= 2x^2+bx+5
    Find the values for b where the graph of f(x):
    1.just touches the x-axis
    2. has two x-intercepts
    3.does not cut or touch the x-axis

    I've tried using the quadratic formula but i have no idea how to do it when there are two unknowns. For number one i thought it must be when y=0 and i've tried substituting other numbers in but other than that i can't start. Can you please start me off?
  2. jcsd
  3. Feb 12, 2007 #2
    When you apply the quadatic formula what are you getting? If [tex] x_{12} = \frac{-b \pm \sqrt{b^2-4ac}}{2a} [/tex] then what does it mean if [tex] x_{12} [/tex] is complex? What about if [tex] x_{12} [/tex] is real? What condition yields a [tex] x_{12} [/tex] as complex? and which condition yields [tex] x_{12} [/tex] as real?
  4. Feb 12, 2007 #3
    b has to be a real number but how can you work it out when there are two unknowns .. x is unknown and so is b
  5. Feb 12, 2007 #4


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    Gold Member

    Using the quadratic formula FrogPad posted, pay special attention to the [tex]b^2-4ac[/tex] part.
  6. Feb 12, 2007 #5


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    You do not need to look at the complete quadratic formula, just the discriminant b2-4ac. Do you know the condition on the discriminant for the equation to have (i)two real roots; (ii) one real repeated root; (iii) no real roots (equivalent to saying the equation has complex roots)?
    Last edited: Feb 12, 2007
  7. Feb 12, 2007 #6
    Yes, but that is before you take into account the 3 subtasks. If a graph touches the x-axis once, how does that affect the number of real solutions to the equation?
  8. Feb 12, 2007 #7
    ooooooook so...
    1. b=square root of 40
    2 b is greater than square root of 40
    3. b is less than square root of 40

    is that right?
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