Question

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

Answer 1

nope

Answer 2

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

Answer 3

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

Answer 4

that didn't work

Answer 5

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

Answer 6

lol....its the french version

Answer 7

that only works for integer roots

Answer 8

Then no wonder it's not mathematically sound. Ahaha

Answer 9

well, for roots that dont incvolve radicals

Answer 10

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

Answer 11

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

Answer 12

\[x=\frac\]

Answer 13

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

Answer 14

but i keep trying to find a counterexample and cant

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

my bad, i forgot to mention sum

Answer 21

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

Answer 22

that was weird lol

Answer 23

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

Answer 24

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

Answer 25

oh ok

Answer 26

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

Answer 27

i have a proof

Answer 28

?

Answer 29

lol, did you just do that?

Answer 30

yes does it make sense?

Answer 31

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

Answer 32

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

Answer 33

lol, your welcome XD

Answer 34

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

Answer 35

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

Answer 36

its really cool :)

Answer 37

by way it works for all numbers