i want to advance read but ai is not helping
#quadratic
verbal creek
brazen lodgeBOT
verbal creek
how do I do basic quadratic equation
earnest sundial
how do I do basic quadratic equation
If you have a particular question you need help with, you can send it here.
simple folio
any examples?
idle totem
how do I do basic quadratic equation
Well there are several levels to this
$$ax^2+bx+c=0$$
halcyon fjordBOT
Calistωo
idle totem
This is the canonical form
We would like to find x
If we start of with a basic example like
$$x^2-d^2=0$$
Then we know that
$$x=\pm d$$
But this means that $x-d$ divides $$x^2-d^2$$
Why? Well suppose this wasnt true. Then we could write
$$x^2-d^2=p(x)(x-d)+r(x)$$
where $p(x)$ and $r(x)$ are just random polynomials of at most degree 1 (lines)
We know that $d$ is a solution to $x^2-d^2$ and $x-d$ so let's plug this in:
$$0=p(d)\cdot 0 +r(x)$$
$$r(x)=0$$
We have derived that our remainder is zero and so there for we have arrived at a contradiction as we a assumed that $(x-d)$ does not divide $x^2-d^2$ but this is only true when $r(x)\neq 0$.
halcyon fjordBOT
Calistωo
idle totem
Why go through all of this rigmarole though?
Well it tells us something important.
$$x^2-d^2=(x-d)(x+d)$$
or for our case, any quadratic can be written as
$$x^2+dx+c=x^2+2(a+b)x+ab$$
For some $a$ and $b$. (this applies when $x^2$ has a nonzero coeff)
halcyon fjordBOT
Calistωo
idle totem
So let's go back to our general case.
$$ax^2+bx+c=0$$
I'm going to do some chicanery to this now.
Divide by a
$$x^2+\frac{b}{a}x+\frac{c}{a}=0$$
add by zero
$$x^2+\frac{b}{a}x+\frac{b^2}{4a^2}-\frac{b^2}{4a^2}+\frac{4ac}{4a^2}=0$$
Collapse the square:
$$\left(x+\frac{b}{2a}\right)^2-\frac{b^2}{4a^2}+\frac{4ac}{4a^2}=0$$
$$\left(x+\frac{b}{2a}\right)^2=\frac{b^2-4ac}{4a^2}$$
simple folio
probably could scaffold better imo, but i have no comments until i know what the OP knows (or doesn't know)
halcyon fjordBOT
Calistωo
idle totem
probably could scaffold better imo, but i have no comments until i know what the...
scaffold?
simple folio
to me, it's like we jumped straight into the meat
i presume the OP has no experience with quadratics
idle totem
fair point ^^'
simple folio
yet we are jumping around between teaching him how to solve, difference of two squares, and completing the squares
idle totem
I was jus trying to give a general intuition for quadratic formula since that just works for any quadratic you would care about
simple folio
don't get me wrong, very insightful explanations (and if you dm i would copy this if anyone asked me or is trolling me)
but i feel like OP might not fully understand right away
my two cents though
idle totem
That's completely valid criticism
simple folio
and given the fact he tried to use AI (so GPT i presume) means that his syllabus and/or teachers might also be failing him, so we have to assume he may be taught in a confusing manner
idle totem
That's fair
simple folio
i do have my personal notes prepared for OP if he needs help, but i'm not sure how clear my notes are for him
earnest sundial
So let's go back to our general case.
$$ax^2+bx+c=0$$
I'm going to do some chi...
DAMN thats dedication
Respect
graceful chasm
DAMN thats dedication
fr
verbal creek
**Calistωo**
it's this one
verbal creek
Well there are several levels to this
mamao not that one
im confused at the
uh
-b±√4abc
–—————
2(1)
how do I do this one
verbal creek
**Calistωo**
i do not get a single thing
ok so guys i tried
uh
ok
so
4ײ-9-7x
ok
right
so
9 and 7 move
so
they be positive
4ײ+7×+9=0
right
and then how do I do the next part
idle totem
-b±√4abc
–—————
2(1)
the quadratic formula is $$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$
halcyon fjordBOT
Calistωo
idle totem
so if $$f(x)=4x^2-7x+9$$
then out solutions are
$$x=\frac{- (-7) \pm \sqrt{(-7)^2-4(4)(9)}}{2(4)}$$
halcyon fjordBOT
Calistωo
idle totem
$$x=\frac{- (-7) \pm \sqrt{(-7)^2-4(4)(9)}}{2(4)}$$
halcyon fjordBOT
Calistωo
idle totem
the plus or minus means there are two solutions here
verbal creek
the plus or minus means there are two solutions here
and at the ± does it stay like that or do I need to change the signs
earnest sundial
ok but why two 7
This comes from the formula
earnest sundial
**Calistωo**
Do you understand this?
idle totem
ok but why two 7
if we have $4x^2-7x+9=0$ then manually solving would look something like this:
halcyon fjordBOT
Calistωo
idle totem
$$4x^2-7x+9=0$$
$$4x^2-7x+\frac{49}{16}+9-\frac{49}{16}=0$$
$$(4x^2-7x+\frac{49}{16})-\frac{49}{16}+\frac{16(9)}{16}=0$$
$$(4x^2-7x+\frac{49}{16})=\frac{49-4(9)(4)}{16}$$
$$\left(2x-\frac{7}{4}\right)^2=\frac{49-4(9)(4)}{16}$$
$$2x-\frac{7}{4}\right=\pm\frac{\sqrt{49-4(9)(4)}}{4}$$
$$2x=\frac{7}{4}\pm\frac{\sqrt{49-4(9)(4)}}{4}$$
$$x=\frac{7 \pm \sqrt{49-4(9)(4)}}{2(4)}$$
$$x=\frac{(-1)^2\cdot7 \pm \sqrt{49-4(9)(4)}}{2(4)}$$
$$x=\frac{-(-7) \pm \sqrt{49-4(9)(4)}}{2(4)}$$
halcyon fjordBOT
Calistωo
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verbal creek
I STILL DONT GET IT 💔💔
I get the gist of it but like
ok
so
ik this one
7x²+3x=0
a is 7 bis 3 c is 0
ok
i also get if it's the wrong uhh
4x²=9+8x
ok
so
4x²-8x-9=0
cause change sign if transverse
am i right
verbal creek
.close