anonymous
  • anonymous
Is it true that for a quadratic equation ax^2+bx+c, the roots of the equation will always equal -b/a?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
nope
amistre64
  • amistre64
-b/a aint even an option...unless you get real lucky lol
myininaya
  • myininaya
it will always be x=frac{-b pm sqrt{b^2-4ac}{2a} a does not equal zero

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myininaya
  • myininaya
that didn't work
anonymous
  • 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
  • amistre64
lol....its the french version
amistre64
  • amistre64
that only works for integer roots
anonymous
  • anonymous
Then no wonder it's not mathematically sound. Ahaha
amistre64
  • amistre64
well, for roots that dont incvolve radicals
anonymous
  • anonymous
And no, not really. You just gotta tweak it.
anonymous
  • anonymous
so it will equal -b/a, assuming I'm only working with integers?
myininaya
  • myininaya
\[x=\frac\]
amistre64
  • amistre64
no.....-b/a aint even on the board
anonymous
  • anonymous
but i keep trying to find a counterexample and cant
amistre64
  • amistre64
-b/2a is a possibility; but that aint always a root unless the graph just touches once
amistre64
  • amistre64
if its a complete square than -b/2a ia the only root
anonymous
  • anonymous
-b/2a is to find the vertex...
anonymous
  • anonymous
i just want to find a counterexample to -b/a being the sum of the roots
amistre64
  • amistre64
-b/2a is the axis of symmetry; but its also half way between roots :)
anonymous
  • anonymous
my bad, i forgot to mention sum
amistre64
  • amistre64
if its a complete square than -b/2a ia the only root
amistre64
  • amistre64
that was weird lol
myininaya
  • 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
  • anonymous
3+2=5, forgot to mention that the sum of the roots = -b/a
myininaya
  • myininaya
oh ok
amistre64
  • amistre64
the quad formula says; stand in the middle at -b/2a....now look left and right an equal distance of sqrt(...)/2a
myininaya
  • myininaya
i have a proof
anonymous
  • anonymous
?
myininaya
  • myininaya
1 Attachment
anonymous
  • anonymous
lol, did you just do that?
myininaya
  • myininaya
yes does it make sense?
anonymous
  • anonymous
yea, do you know how it can be useful though?
myininaya
  • 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
  • anonymous
lol, your welcome XD
myininaya
  • 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
  • anonymous
I am. My sis just brought this to my attention and I never realized it before. XD
myininaya
  • myininaya
its really cool :)
myininaya
  • myininaya
by way it works for all numbers

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