1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Without solving the equation, find the value of the roots

  1. Oct 14, 2013 #1
    1. The problem statement, all variables and given/known data

    23 - 5x - 4x2 = 0

    find ([itex]\alpha[/itex] - [itex]\beta[/itex])2

    2. Relevant equations

    In previous parts of the question i've calculated [itex]\alpha[/itex] + [itex]\beta[/itex], [itex]\alpha[/itex][itex]\beta[/itex], 1/[itex]\alpha[/itex] + 1/[itex]\beta[/itex] and ([itex]\alpha[/itex]+1)([itex]\beta[/itex]+1) but I can't think of any rules I know to help me solve the problem.

    3. The attempt at a solution

    Expanding ([itex]\alpha[/itex] - [itex]\beta[/itex])2


    [itex]\alpha[/itex]2+[itex]\beta[/itex]2 -2[itex]\alpha[/itex][itex]\beta[/itex]

    But I don't know what I can do with this info.

    I'd appreciate a nudge in the right direction!

  2. jcsd
  3. Oct 14, 2013 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You can write your expression fairly simply in terms of [itex] \alpha+\beta [/itex] and [itex] \alpha \beta [/itex] (from which you can get the final answer according to your part 2)
  4. Oct 14, 2013 #3


    Staff: Mentor

    ##(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta##
    You said that you have already calculated ##\alpha + \beta ## and ##\alpha\beta ##.
  5. Oct 14, 2013 #4
    Gah, I should have seen that.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted