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Quadratic functions

  • Thread starter wellY--3
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  • #1
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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?
 

Answers and Replies

  • #2
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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?
 
  • #3
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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
 
  • #4
danago
Gold Member
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Using the quadratic formula FrogPad posted, pay special attention to the [tex]b^2-4ac[/tex] part.
 
  • #5
cristo
Staff Emeritus
Science Advisor
8,107
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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:
  • #6
664
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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
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?
 
  • #7
12
0
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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