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!

Would this be sufficient as a proof?

  1. Jul 21, 2016 #1
    1. The problem statement, all variables and given/known data
    Capture.png

    2. Relevant equations
    Vieta's formula, quadratic discriminant

    3. The attempt at a solution
    test.png

    test3.png

    test4.png

    teste.png
     
  2. jcsd
  3. Jul 22, 2016 #2

    Ssnow

    User Avatar
    Gold Member

    suggestion for the first part: since ##\alpha,\beta## are solutions your equation as also a second form ##(x-\alpha)(x-\beta)=0## so you can expand this and proceed comparing with ##ax^{2}+2bx+c=0## ...
    for the second part you must to look to the ##\Delta## of the equation ##ax^{2}+2mbx+nc=0## and to prove that is ##\geq 0## (observe that ##b^{2}-ac\geq 0## by assumption) ...

    Your attempt at a solution is very long, I hope with my suggestions you will able to simplify ...
     
  4. Jul 25, 2016 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I was a bit confused because the order of the solution attachments does not match the order of the questions. The last attachment appears to address the first question. As Ssnow writes, it is simpler to start with factorisation.

    The first attached solution seems unrelated to the posted questions.

    The second attached solution does seem to be related to the second posted question, but exactly how is unclear.

    The third attached solution does address the second question, but the logic is backwards. You are asked to show that the equation has real roots, so you should not start with "if it has real roots". You could start with "it will only have real roots if..."
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Would this be sufficient as a proof?
  1. Sufficient Estimators (Replies: 8)

Loading...