Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quadratic formula

  1. Jan 5, 2008 #1
    Regarding [tex]\displaystyle{\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

    How should "[tex]\displaystyle{\pm}[/tex]" be treated?

    I know a square root can be both possitive and negative, but does the quardratic forumla dictate that a possitive root should be added to -b, or does it dictate that a postive root should be subtracted from -b???
  2. jcsd
  3. Jan 5, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The quadradic forumal yields 2 roots. You do both.
  4. Jan 5, 2008 #3

    Gib Z

    User Avatar
    Homework Helper

    Some people get confused because other times they see the plus/minus sign, they have to choose correctly, whilst in this case you do it both. Thats why you may also see the formula written as;

    [tex]x_1= \displaystyle{\frac{-b + \sqrt{b^2 - 4ac}}{2a}}[/tex]

    [tex]x_2 = \displaystyle{\frac{-b - \sqrt{b^2 - 4ac}}{2a}}[/tex]
  5. Jan 5, 2008 #4
    Sorry, I'm a little confused.

    Say a particular solution to a quadratic equation is [tex]\displaystyle{\frac{2 \pm \sqrt{7}}{3}}[\tex]

    If 7 was a perfect sqaure, would the root get added to or subtrected from 2?
  6. Jan 5, 2008 #5

    Gib Z

    User Avatar
    Homework Helper

    It doesn't matter if 7 is a perfect square or not (and it isn't). There are TWO roots to a quadratic equation, hence the quadratic formula has TWO solutions. One of the solutions is when you add the square root part, the other solution is when you subtract it. Look at my previous post.
  7. Jan 5, 2008 #6
    Okay I've got it. The 2 solutions are adding a possitive root, and subtracting a possitive root, correct? (Subtracting a negative root is = to adding it, adding a negative root is = to subtracting it).
  8. Jan 5, 2008 #7


    User Avatar
    Science Advisor
    Homework Helper

    [itex]\sqrt{x}[/itex] is used to denote the positive square root of x. Thus [itex]\sqrt{4}=2[/itex] is correct while [itex]\sqrt{4}=\pm2[/itex] is incorrect. Thinking that the latter is correct is too common a mistake - make sure you aren't making it.
  9. Jan 5, 2008 #8
    Got it, thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook