quadratic | Mathematics | Page 1

clever canopyBOT Apr 4, 2024, 2:35 AM

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weary jungle Apr 4, 2024, 2:39 AM

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what is the distance between the two roots? and can you express this as only a function in terms of t

mighty hound Apr 4, 2024, 2:43 AM

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weary jungle what is the distance between the two roots? and can you express this as only a f...

how though

weary jungle Apr 4, 2024, 2:43 AM

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that’s up to you to figure out

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if not i’ll give a hint in a bit

mighty hound Apr 4, 2024, 2:43 AM

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ive already tried i end up with inequalities using the discrminant

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if i had two definite values of t i wouldve subbed it into the eqn to find the x intercepts and calculate the distance

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but right now i have t<0 and t>6

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these are unbounded

mighty hound Apr 4, 2024, 2:45 AM

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weary jungle if not i’ll give a hint in a bit

i cant figure it out

weary jungle Apr 4, 2024, 2:45 AM

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how can you find the exact value of the roots?

mighty hound Apr 4, 2024, 2:45 AM

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y=0

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but then we need a value of t. i used the discriminant b^2-4ac>0

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do u suggest i just use t=0 and t=6? @weary jungle

weary jungle Apr 4, 2024, 2:48 AM

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nope

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exact value

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no matter the value of t

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think!!

mighty hound Apr 4, 2024, 2:48 AM

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i have 😭

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i need help pls can i have the hint. after subbing y=0 or using the discriminant i literally dont know what to do @weary jungle

weary jungle Apr 4, 2024, 2:49 AM

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what’s the discriminant part of

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what big thing

mighty hound Apr 4, 2024, 2:50 AM

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quadratic eqn

weary jungle Apr 4, 2024, 2:50 AM

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yes!

mighty hound Apr 4, 2024, 2:50 AM

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so i can still use t

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in my quadratic eqn

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pleasssse

weary jungle Apr 4, 2024, 2:53 AM

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yup, those are the roots, so what’s the distance?

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and how can you find the max of the function?

mighty hound Apr 4, 2024, 2:53 AM

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weary jungle yup, those are the roots, so what’s the distance?

i dont know how to find the distance if its in terms of t

weary jungle Apr 4, 2024, 2:54 AM

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okay we have two roots a and b

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what’s the distance

mighty hound Apr 4, 2024, 2:54 AM

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b-a

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okay so i find the distance

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in terms of t

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@weary jungle

weary jungle Apr 4, 2024, 2:55 AM

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yea

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now you need to find its maximum

mighty hound Apr 4, 2024, 2:56 AM

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weary jungle now you need to find its maximum

max of a fraction in this case is when numerator maximum

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isnt that when t -> infinity

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@weary jungle

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how do i find the max

weary jungle Apr 4, 2024, 2:57 AM

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well no since-4t^2+24t is a downward quadratic

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but even then remember the range you put on t

mighty hound Apr 4, 2024, 3:00 AM

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weary jungle well no since-4t^2+24t is a downward quadratic

t<0 and t>6

solving that gives t=6, t=0

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which are the critical values i found from the discriminant

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i genuinely dont know how to find the max could you please outline the process

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@weary jungle

weary jungle Apr 4, 2024, 3:01 AM

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so what does this cancel into

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what do you get

mighty hound Apr 4, 2024, 3:01 AM

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0/2

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wait no

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this

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plus this

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@weary jungle

weary jungle Apr 4, 2024, 3:02 AM

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yup

mighty hound Apr 4, 2024, 3:02 AM

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will it still be over 2

weary jungle Apr 4, 2024, 3:02 AM

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it’s actually just one of that since like

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2sqrtthing/2

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sqrtthing

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super convenient ngl

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now what’s inside is a quadratic facing downwards, correct?

mighty hound Apr 4, 2024, 3:03 AM

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weary jungle now what’s inside is a quadratic facing downwards, correct?

i mean the quadratic inside the root is facing down

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if thats what you mean

mighty hound Apr 4, 2024, 3:03 AM

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weary jungle it’s actually just one of that since like

how

weary jungle Apr 4, 2024, 3:03 AM

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yes

mighty hound Apr 4, 2024, 3:03 AM

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youre adding two positive things

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why would one just go

weary jungle Apr 4, 2024, 3:03 AM

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you’re dividing 2 remember

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$\frac{\sqrt u+\sqrt u}{2}=\frac{2\sqrt u}{2}=\sqrt u$

steel talonBOT Apr 4, 2024, 3:04 AM

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!𒐪 ɹɐupoɯ⇂ㄥ8𝟝 𒐪!

mighty hound Apr 4, 2024, 3:05 AM

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weary jungle $\frac{\sqrt u+\sqrt u}{2}=\frac{2\sqrt u}{2}=\sqrt u$

makes sense

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then what do you do

weary jungle Apr 4, 2024, 3:06 AM

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find the maximum value of the function inside

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yk how to do that right

mighty hound Apr 4, 2024, 3:06 AM

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weary jungle yk how to do that right

the turning point

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(3,36)

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@weary jungle

weary jungle Apr 4, 2024, 3:07 AM

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nice, so what’s the value of t that makes the distance the greatest

mighty hound Apr 4, 2024, 3:08 AM

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weary jungle nice, so what’s the value of t that makes the distance the greatest

is it 3

weary jungle Apr 4, 2024, 3:09 AM

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yea

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that’s what you solved for

mighty hound Apr 4, 2024, 3:09 AM

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weary jungle yea

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that doesnt satisfy

weary jungle Apr 4, 2024, 3:09 AM

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oh i forgot i thought it was the other way

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wait wait hold up

weary jungle Apr 4, 2024, 3:10 AM

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mighty hound plus this

isn’t THIS the discriminant??

mighty hound Apr 4, 2024, 3:10 AM

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the discriminant is b^2-4ac>0 as it has two roots

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so (4t)^2 - 4(1)(5t^2-6t) > 0

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which leads to t<0 and t>6

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@weary jungle

weary jungle Apr 4, 2024, 3:11 AM

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try testing a t>6

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does it provide two roots?

mighty hound Apr 4, 2024, 4:11 AM

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i got it now

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nvm

night field Apr 4, 2024, 6:59 AM

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@quartz roost shiii bruh is this from the Dilcue contest as well?

quartz roost Apr 4, 2024, 7:01 AM

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Holy shit

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Yo @mighty hound all these problems are on the dilcue contest do you wanna see the link?

mighty hound Apr 4, 2024, 7:10 AM

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uhhh

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nvm

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i think i understand it

weary jungle Apr 4, 2024, 7:33 AM

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night field <@1058261446431092756> shiii bruh is this from the Dilcue contest as well?

oh 💀

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thats a CONTEST question?

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looks liek your normal class question 💀

#quadratic