Why is delta used in the equation for the discriminate?

[vanmaiden]

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 occurring?

 

[Ray Vickson]

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

 

[NascentOxygen]

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 occurring?

I'd forgotten that delta is sometimes used, but thanks for the reminder.

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.

 

[PeterO]

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 occurring?

No change - it is just shorter - sort of like a name for the dicriminant.

 

[Mark44]

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.

 

[vanmaiden]

I'd forgotten that delta is sometimes used, but thanks for the reminder.

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.

 

[NascentOxygen]

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.)

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.)