Parameters

[obtuse socket]

I've done most calculations but I don't think correctly

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[obtuse socket]

They're asking us to find all values of m for which

That equation has 2 different, positive roots x1 and x2

And they have to be this

This is what I've done

[random sable]

Have you tried solving the quadratic equation?

[stone panther]

Why didn't you finish the discriminant calculation?

[obtuse socket]

The one on the bottom? It just says m is all real numbers I assumed that's wrong 😭

Or at least unimportant

Or um

[random sable]

You can simplify the discriminant more. I'd solve the quadratic

[obtuse socket]

Sorry what's a discriminant?

[random sable]

The thing inside the square root

[obtuse socket]

Oh but where is that in all of this?

[random sable]

The thing you're saying it has to be > 0

Is what is inside the square root

Second line

[obtuse socket]

Oh well won't it just come out to be 36 > 0? Or did I do something wrong

[random sable]

Exactly

That means just means there are always 2 unique solutions

Now to know the solutions, you have to solve the quadratic

[obtuse socket]

Which oneeee

I've got this from the bottom one

Ooh I think I know what I might've done wrong

No never mind I don't 😭

[random sable]

I think some signs are flipped there

So you squared the left expression, right?

[obtuse socket]

Yes

[random sable]

Shouldn't the m^2 be positive and the m negative?

[obtuse socket]

Oh yes 😭

[obtuse socket]

Okay I'll work from here ty

[random sable]

No problem

[obtuse socket]

But also don't we have to

[obtuse socket]

Make sure the roots are positive?

I don't know how to account for that part

[random sable]

Are they asking for the roots to be positive?

[obtuse socket]

Yes

[random sable]

I'd just calculate the roots then

[obtuse socket]

But how if we don't know the m

[random sable]

You can use the quadratic equation

And substitude b = (2-4m)

And c = (m^2-m-2)

I'm trying to think of another way of making sure the roots are positive

[obtuse socket]

Okayy while I'm trying to understand this one hahah 😭

Oh like using those

[obtuse socket]

Viete's formulas?

[random sable]

You can also use Viete's formula

But this is what I'm talking about

[obtuse socket]

This is just like

The regular delta and finding roots thing

[obtuse socket]

I think this would be betterrr

[random sable]

Yeah

You need to know if the roots are positive

So you need to know the roots

It simplifies quite nicely

[obtuse socket]

Oh it does

?

I'd rather do the viete thing thoughh 😭

It looks so simple

If I wrote it down correctly

[random sable]

Yeah that's correct

[obtuse socket]

Okayy goodd

[random sable]

Yeah that'd work. If they're both positive, then their product has to be positive

And their sum has to be positive

You gotta solve those equations, then

[obtuse socket]

Yes I've just finished

Sooo adding all those groups together and the previous one

That's the answerr?

[random sable]

Wait wait, here you simplified the m^2 but they don't simplify, do they?

[obtuse socket]

Oh...

True

😭

You're very perceptive omg

Let me fix that part waitt

[random sable]

Nahhh I just solved it too so I can see if the equations are the same or not haha

[obtuse socket]

That's great help omg

[obtuse socket]

That's what I got heree

[random sable]

-4m -2(-m) = -2m, not 2m

[obtuse socket]

Oh right

This is embarrassing 😭

[random sable]

Nahh algebra is so annoying

[obtuse socket]

YEAH

[random sable]

There's also one other thing

[random sable]

Here, you need both things to be true

So the first one is telling you
m in (-infty, -1) u (2, +infty)
And the second one is telling you
m in (-0.5, +infty)

You have to get the interval where both are true

[obtuse socket]

Ohh yes

I thought that but I kinda forgot that

[obtuse socket]

Good?

[random sable]

Yeee

[random sable]

So now you need to find both things to be true

[obtuse socket]

Final result

[random sable]

Does > mean it is included and ( means it is not included?

[obtuse socket]

Yes

[random sable]

Yeee it's great then

[obtuse socket]

Okayy yay

Tysmm

+close

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