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C1 question on terminology

So, I was just thinking to myself, you know, as you do: if a question states an equation has real roots does that mean the discriminant is

b^2-4ac \geq 0

or does it mean

b^2-4ac > 0

It doesn't specify that it has equal / different real roots so it should be

b^2-4ac \geq 0

Right?

Reply 1

Zacken

Original post by Kozmo

So, I was just thinking to myself, you know, as you do: if a question states an equation has real roots does that mean the discriminant is

b^2-4ac \geq 0

or does it mean

b^2-4ac > 0

It doesn't specify that it has equal / different real roots so it should be

b^2-4ac \geq 0

Right?

If it doesn't specify distinct roots then when it says a quadratic has real roots then the discriminant is

b^2 - 4ac \geq 0

since real and equal roots are still real roots.

Reply 2

KaylaB

Original post by Kozmo

So, I was just thinking to myself, you know, as you do: if a question states an equation has real roots does that mean the discriminant is

b^2-4ac \geq 0

or does it mean

b^2-4ac > 0

It doesn't specify that it has equal / different real roots so it should be

b^2-4ac \geq 0

b^2-4ac \geq 0

as if it is equal to zero it still has one root, which is still a real root

Spoiler

(edited 8 years ago)

Reply 3

sammyyrosee

Well yes, since equal roots would mean the discriminate is equal to zero.

:smile:

Reply 4

Zacken

Original post by KaylaB

Spoiler

There was a whole two minute gap. :teehee:

Reply 5

KaylaB

Original post by Zacken

There was a whole two minute gap. :teehee:

I think you'll find it was a one minute gap :closedeyes:

Spoiler

Reply 6

Kozmo

Original post by Zacken

If it doesn't specify distinct roots then when it says a quadratic has real roots then the discriminant is

b^2 - 4ac \geq 0

since real and equal roots are still real roots.

Original post by KaylaB

b^2-4ac \geq 0

as if it is equal to zero it still has one root, which is still a real root

Spoiler

Original post by sammyyrosee

Well yes, since equal roots would mean the discriminate is equal to zero.

:smile:

Yep, thought so, thanking you all! :smile:

Reply 7

Zacken

Original post by Kozmo

Yep, thought so, thanking you all! :smile:

You're very welcome! :smile:

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C1 question on terminology

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