## anonymous 5 years ago Is it true that for a quadratic equation ax^2+bx+c, the roots of the equation will always equal -b/a?

1. amistre64

nope

2. amistre64

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

3. myininaya

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

4. myininaya

that didn't work

5. 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

6. amistre64

lol....its the french version

7. amistre64

that only works for integer roots

8. anonymous

Then no wonder it's not mathematically sound. Ahaha

9. amistre64

well, for roots that dont incvolve radicals

10. anonymous

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

11. anonymous

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

12. myininaya

$x=\frac$

13. amistre64

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

14. anonymous

but i keep trying to find a counterexample and cant

15. amistre64

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

16. amistre64

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

17. anonymous

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

18. anonymous

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

19. amistre64

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

20. anonymous

my bad, i forgot to mention sum

21. amistre64

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

22. amistre64

that was weird lol

23. 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

24. anonymous

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

25. myininaya

oh ok

26. amistre64

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

27. myininaya

i have a proof

28. anonymous

?

29. myininaya

30. anonymous

lol, did you just do that?

31. myininaya

yes does it make sense?

32. anonymous

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

33. 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

34. anonymous

35. 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

36. anonymous

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

37. myininaya

its really cool :)

38. myininaya

by way it works for all numbers