conditions required

niharika_kumar · 2014-06-09 22:36:40

What are the conditions required for a quadratic equation to be positive?

Agnishom · 2014-06-09 23:19:10

You mean the roots of the equation to be positive?

Agnishom · 2014-06-09 23:37:48

Let the equation be

For positive roots,

Last edited by Agnishom (2014-06-09 23:41:35)

ShivamS · 2014-06-10 00:42:07

If you mean all the values of the quadratic equation, you would need to read about linear algebra, Sylvester's criterion etc.

Agnishom · 2014-06-10 01:18:39

Why? My solution does not work?

ShivamS · 2014-06-10 01:51:41

It works only for the roots of the equation.

anonimnystefy · 2014-06-10 03:21:24

For a quadratic to always be positive you need:

and

For a quadratic to have positive roots, you need the conditions Agnishom posted, except, the second condition should be

Last edited by anonimnystefy (2014-06-10 03:25:12)

ShivamS · 2014-06-10 03:48:23

ShivamS wrote:

If you mean all the values of the quadratic equation, you would need to read about linear algebra, Sylvester's criterion etc.

This works for the general form of a quadratic equation (i.e. ax^2 + bx + cy^2 + dy + exy + f > 0).

Last edited by ShivamS (2014-06-10 03:56:02)

anonimnystefy · 2014-06-10 03:53:18

Well, I really don't think that's what he's looking for right now.

And, aren't you missing a term there?

ShivamS · 2014-06-10 03:55:02

Thanks.

Last edited by ShivamS (2014-06-10 03:55:13)

anonimnystefy · 2014-06-10 04:16:51

Nessun problema.

niharika_kumar · 2014-06-10 20:35:23

anonimnystefy wrote:

For a quadratic to always be positive you need:

and

I wanted this.
thanks

Can you explain more on why is it so.

Last edited by niharika_kumar (2014-06-10 20:36:07)

anonimnystefy · 2014-06-11 00:09:04

Hi nikarika_kumar

Look at the graph of a parabola which is always positive.

Notice that it cannot have any intersection with the x-axis. If it did, there would be points where it is 0 and/or negative, which we don't want.

So, this leads us to conclude that, because the parabola has no intersections with the x-axis,

.

Also, another thing we need to notice is the orientation of the parabola. If it has no solutions and is upside down from the picture above, it will always be negative:

So, we need the parabola to be turned like in the first picture. That will happen when

.

That's all there is to it.

Last edited by anonimnystefy (2014-06-11 00:10:11)

Agnishom · 2014-06-11 00:56:03

niharika_kumar wrote:

What are the conditions required for a quadratic equation to be positive?

She means polynomial

ShivamS · 2014-06-11 04:41:20

That was to be assumed.

anonimnystefy · 2014-06-11 05:04:12

Yeah.

niharika_kumar · 2014-06-11 21:14:46

thanks for the clear explaination.

anonimnystefy · 2014-06-12 00:22:48

No problem. I'm glad it was clear. I tend to complicate.

Math Is Fun Forum

#1 2014-06-09 22:36:40

conditions required

#2 2014-06-09 23:19:10

Re: conditions required

#3 2014-06-09 23:37:48

Re: conditions required

#4 2014-06-10 00:42:07

Re: conditions required

#5 2014-06-10 01:18:39

Re: conditions required

#6 2014-06-10 01:51:41

Re: conditions required

#7 2014-06-10 03:21:24

Re: conditions required

#8 2014-06-10 03:48:23

Re: conditions required

#9 2014-06-10 03:53:18

Re: conditions required

#10 2014-06-10 03:55:02

Re: conditions required

#11 2014-06-10 04:16:51

Re: conditions required

#12 2014-06-10 20:35:23

Re: conditions required

#13 2014-06-11 00:09:04

Re: conditions required

#14 2014-06-11 00:56:03

Re: conditions required

#15 2014-06-11 04:41:20

Re: conditions required

#16 2014-06-11 05:04:12

Re: conditions required

#17 2014-06-11 21:14:46

Re: conditions required

#18 2014-06-12 00:22:48

Re: conditions required

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