Is it true that for a quadratic equation ax^2+bx+c, the roots of the equation will always equal -b/a?

- anonymous

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- amistre64

nope

- amistre64

-b/a aint even an option...unless you get real lucky lol

- myininaya

it will always be x=frac{-b pm sqrt{b^2-4ac}{2a}
a does not equal zero

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## More answers

- myininaya

that didn't work

- anonymous

There is a sort of cheat way to factor it though. I'm told it's not technically mathematically sound, but I like it and it works.
Multiply a and b

- amistre64

lol....its the french version

- amistre64

that only works for integer roots

- anonymous

Then no wonder it's not mathematically sound. Ahaha

- amistre64

well, for roots that dont incvolve radicals

- anonymous

And no, not really. You just gotta tweak it.

- anonymous

so it will equal -b/a, assuming I'm only working with integers?

- myininaya

\[x=\frac\]

- amistre64

no.....-b/a aint even on the board

- anonymous

but i keep trying to find a counterexample and cant

- amistre64

-b/2a is a possibility; but that aint always a root unless the graph just touches once

- amistre64

if its a complete square than -b/2a ia the only root

- anonymous

-b/2a is to find the vertex...

- anonymous

i just want to find a counterexample to -b/a being the sum of the roots

- amistre64

-b/2a is the axis of symmetry; but its also half way between roots :)

- anonymous

my bad, i forgot to mention sum

- amistre64

if its a complete square than -b/2a ia the only root

- amistre64

that was weird lol

- myininaya

so you want to find a counterexample:
how about x^2-5x+6=0
-b/a=5
but there are two solutions and neither of them are 5
the solutions are x=3 and x=2

- anonymous

3+2=5, forgot to mention that the sum of the roots = -b/a

- myininaya

oh ok

- amistre64

the quad formula says; stand in the middle at -b/2a....now look left and right an equal distance of sqrt(...)/2a

- myininaya

i have a proof

- anonymous

?

- myininaya

##### 1 Attachment

- anonymous

lol, did you just do that?

- myininaya

yes does it make sense?

- anonymous

yea, do you know how it can be useful though?

- myininaya

you can use it to sort of check yourself
instead of plugging your answers back into the equation to check
you can just see they add up to be -b/a
thanks for pointing this out
i never realized it before

- anonymous

lol, your welcome XD

- myininaya

the square roots cancel because one was postive and one was negative
just like 5+(-5)=0
so you completely understand?
thats amazing
well unless you are passed algebra by now

- anonymous

I am. My sis just brought this to my attention and I never realized it before. XD

- myininaya

its really cool :)

- myininaya

by way it works for all numbers

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