Discriminant

[cloud fog]

Can someone help me with the thought process

[cloud fog]

This is the soluition

but i dont get about how if theres one soluition for u then there miught be 2 solutions for x

i understand x^2=u

and that x=plus or minus sqrt of U

[signal verge]

If you let u = 4, then we get
x^2 = 4
⇒ x = ±sqrt(4)

That’s why if there’s one solution for u, then there could be two solutions for x

[cloud fog]

Ohh yeah

Thank u

[cloud fog]

Ad if theres 2 solution for u theres a possibility of 4 solutions for x

but we only want 2 so one has to be negative for it to not count as a real number?

[jade tiger]

If u=0, then there’s only 1 solution for x

[covert oasis]

So for 2 real solution let t=x². Then t²-t+k=0 it's parabola which vertex on the right side at y. Then for 2 solutions you need 1 positive solution in u. So this parabola should negative at 0. So k<0

[cloud fog]

Are u able to draw this out pls?

[jade tiger]

$t^{2}-t+k=(t-\frac{1}{2})^{2}-\frac{1}{4}+k$

[fleet bramble]

BBMaths

[cloud fog]

Okay this gives us (1/2,-1-4) as the min

[jade tiger]

K-1/4

[cloud fog]

I dont understand

[jade tiger]

$t^{2}-t+k=(t-\frac{1}{2})^{2}-\frac{1}{4}+k =(t-\frac{1}{2})^{2}+(k-\frac{1}{4})$

[fleet bramble]

BBMaths

[cloud fog]

yes i see

What does this mean tho

😭😭😭

[jade tiger]

You need 1 solution, so you want the minimum point to be exactly at y=0

[cloud fog]

ohhh

Yes i see now

[cloud fog]

I understand y=0 but how soes this come to K<0

[jade tiger]

That’s one of the cases but we must of missed something to miss out k<0

We did t=x^2 which means that we only need t>=0

So if the quadratic in t has negative roots we don’t count them

[teal plover]

sorry to disrupt but what level is this?

of math *

[cloud fog]

Im 17

Its like As level ig

As-A2 alevel

[teal plover]

ok

[cloud fog]

?

Its for the oxfod admission test

Oxford

[teal plover]

ohh tmua

[cloud fog]

Its MAY

MAT

[teal plover]

oh

uhhh good luck gng

[jade tiger]

If we want only one solution in t we can also get away with it if we have one root of t<0

[teal plover]

(what course u applying for?)

[cloud fog]

Im doing maths+cs

[cloud fog]

Hmm

[jade tiger]

If k is 0 then t=0 is a root but we want negative t, so we need k even more negative than that

[cloud fog]

Hmm

[jade tiger]

So k<0 also works

I did t notice that until I read the answer

[cloud fog]

Yeah

Really?

I wnana study maths there too

[jade tiger]

I got 88 in mat

[cloud fog]

Holy lovked

How long did u study for MAT?

And how did u study for it

ngl i js started studying start of aept

Sept

[jade tiger]

I don’t remember but I do remember that I got a question wrong about circles and lines and I got the right answer immediately but then I talked myself out of it and lost 4 marks

[cloud fog]

Crazy

[teal plover]

What were ur gcse grades

[cloud fog]

Prolly 7-9s

Gcses dont even matter

Its abt MAT and alvls ig

[teal plover]

I wanna go top 5 uni but I was too busy playing Roblox for GCSEs

[cloud fog]

🤣🤣🤣i was too

[teal plover]

[cloud fog]

I got all 7+ even tho i barely revised tho

Gcses dont matter

Js focus on ur alevels

Aslong as u passed most

And got a couple As

[teal plover]

My school factors them in for a level predicteds 😓

[jade tiger]

It was question J on 2022 paper

[cloud fog]

How long were u prepping for it?

[jade tiger]

I got IGCSE A* in year 7

Then A* a level maths in year 10

[cloud fog]

Crazy

[teal plover]

🫩

[cloud fog]

These the people im competing with

[teal plover]

How

[cloud fog]

Ngl i could of got A* in maths in y9 but my teachers all ahh

[jade tiger]

Then I stalled during covid

[cloud fog]

How did u prepare for MAT?

[jade tiger]

I did lots of past papers

I don’t remember really

[cloud fog]

Ohh

Alr fair enough

[jade tiger]

!done

[twilit hamlet]

If you are done with this channel, please mark your problem as solved by typing .close

[charred nexus]

Maybe dat?

I don't know what "two real solutions" means. It means the solutions don't have to be the same. Because we could say that if D == 0, then we simply have two identical solutions, but we're simply saying there's only one solution.

🤯

@cloud fog are you here?

[cloud fog]

Yeah

i js finsihed work

Illl look at it ina bit

[charred nexus]

k

[cloud fog]

What does hat bottom line mean

[charred nexus]

ok

i missed o

[cloud fog]

I meant on ur image🤣🤣🤣

The last bit

[cloud fog]

The answer is k<0 and k=1/4

[charred nexus]

i didnt see

[jade tiger]

it’s not (-infinity,1/4) because 0 is not a solution and 1/4 is

!done (When you’re done)

[twilit hamlet]

If you are done with this channel, please mark your problem as solved by typing .close

[charred nexus]

This is the first time I've completed this kind of task, so there must be some nuances that I'm not aware of

i tried

[cloud fog]

Ah the k is only for t. We need it for X

So u only done a bit of the work

[cloud fog]

-close

[jade tiger]

.close

[cloud fog]

.close