# Delta with discriminate

## Homework Statement

With the discriminate, why is delta sometimes used?

## Homework Equations

$\Delta$ = 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

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Ray Vickson
Homework Helper
Dearly Missed
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
Staff Emeritus
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.

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:
PeterO
Homework Helper

## Homework Statement

With the discriminate, why is delta sometimes used?

## Homework Equations

$\Delta$ = 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.

Mark44
Mentor
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.

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
Staff Emeritus
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.)