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Delta with discriminate

  • Thread starter vanmaiden
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  • #1
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Homework Statement


With the discriminate, why is delta sometimes used?


Homework Equations


[itex]\Delta[/itex] = b2 - 4ac


The Attempt at a Solution


I get the logic behind what the discriminate is and how and why it works, but I don't understand why delta is used in the equation. What change is occuring?
 

Answers and Replies

  • #2
Ray Vickson
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Nothing is changing. They need to have some symbol for the discriminant, and they have decided to use Delta (Greek D for Discriminant). I have never seen that notation, but it does make some sense.

RGV
 
  • #3
NascentOxygen
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I get the logic behind what the discriminate is and how and why it works, but I don't understand why delta is used in the equation. What change is occuring?
I'd forgotten that delta is sometimes used, but thanks for the reminder. :smile:

It's probably as good a choice as any, because the discriminant relates directly to the step either side of the peak in the parabola where it crosses the axis.

i.e., x = -b +/- sqrt(b2 -4ac) ....etc

So, the offset up (and down) about -b/(2a) is determined by delta. To be exact, delta/(2a)

If the coefficient of x is unity, then delta actually is the distance between the roots. If delta = 0 then the roots coincide; there is no distance between them.
 
Last edited:
  • #4
PeterO
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Homework Statement


With the discriminate, why is delta sometimes used?


Homework Equations


[itex]\Delta[/itex] = b2 - 4ac


The Attempt at a Solution


I get the logic behind what the discriminate is and how and why it works, but I don't understand why delta is used in the equation. What change is occuring?
No change - it is just shorter - sort of like a name for the dicriminant.
 
  • #5
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Nothing is changing. They need to have some symbol for the discriminant, and they have decided to use Delta (Greek D for Discriminant). I have never seen that notation, but it does make some sense.
It's probably as good a choice as any, because the discriminant relates directly to the step either side of the peak in the parabola where it crosses the axis.

i.e., x = -b +/- sqrt(b2 -4ac) ....etc
I believe that delta is used only because the word discriminant starts with "d", the same sound as the letter delta represents.
 
  • #6
102
1
I'd forgotten that delta is sometimes used, but thanks for the reminder. :smile:

It's probably as good a choice as any, because the discriminant relates directly to the step either side of the peak in the parabola where it crosses the axis.

i.e., x = -b +/- sqrt(b2 -4ac) ....etc

So, the offset up (and down) about -b/(2a) is determined by delta. To be exact, delta/(2a)

If the coefficient of x is unity, then delta actually is the distance between the roots. If delta = 0 then the roots coincide; there is no distance between them.
Hey, could you elaborate on the "offset up and down" portion? I've never seen that terminology used with parabola's before.
 
  • #7
NascentOxygen
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Hey, could you elaborate on the "offset up and down" portion? I've never seen that terminology used with parabola's before.
Well, this gives me the opportunity to make a correction to what I wrote. (Sharp eyes would have noted that I omitted the essential string sqrt in one or two places.)
me said:
It's probably as good a choice as any, because the discriminant relates directly to the step either side of the peak in the parabola where it crosses the axis.

i.e., x = -b +/- sqrt(b2 -4ac) ....etc

So, the offset up (and down) about -b/(2a) is determined by delta. To be exact, sqrt of delta/(2a)

If the coefficient of x2 is unity, then sqrt of delta actually is the distance between the roots. If delta = 0 then the roots coincide; there is no distance between them.
Harking back to your first encounter with graphing the parabola, you found that the parabola's minimum (or maximum) occurs where x=-b/(2a)
and the parabola crosses the x-axis at two points offset from this by an amount +/- sqrt(b2 - 4ac)/(2a)

So you can see this offset is directly related to delta. (To the square root of delta, to be more precise.)
 

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