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: Finding for k in quadratic equation.

  1. Aug 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the least integral value of k for which the quadratic polynomial
    (k-2)x2 + 8x + k+4 > 0 where x is real.

    3. The attempt at a solution

    i am trying to solve the discriminant by equating it to>0
    but i don't think it is correct.
    Please provide hints for this solutions.
  2. jcsd
  3. Aug 23, 2011 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Show us what you have done.
  4. Aug 23, 2011 #3

    as x is real

    .'. 64-4(k-2)(k+4)>0

    on solving
    i got

    after that what should I do

    should i find the values of k from this inequality???
  5. Aug 23, 2011 #4


    User Avatar
    Homework Helper

    No, it's not... at least the way I'm interpreting the question.

    You are looking for the smallest integer k such that, if you plug in ANY REAL NUMBER for x, the quadratic becomes positive. That means that the graph of the parabola would be entirely above the x-axis. What does that say about the discriminant?
  6. Aug 23, 2011 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You might want to check your algebra on trying to solve for k in the inequality. What happened to the constant 64?
  7. Aug 23, 2011 #6


    User Avatar
    Homework Helper

    The algebra is actually correct. The OP multiplied the binomials, combined like terms, and then divided both sides by -4. The inequality symbol used in the beginning is wrong, however.
  8. Aug 23, 2011 #7
    the smallest value of the function:[tex]f(x)=ax^2+bx+c=0[/tex]


    [tex]\frac {-D}{4a}[/tex]

    to get this value positive D should be negative-------------(I)
    and solving according this we get
    64-4(k-2)(k+4) < 0
    as this may result in correct answer

    but as x is real .'. D should be positive or zero--------------(II)

    I am confused with (I) (II)
    Last edited: Aug 23, 2011
  9. Aug 23, 2011 #8
    i got the answer
    by using this


    before i was running on the wrong concept:confused:

    now i got the answer
    thank you very much for your valuable suggestion and valuable time for me

    thank you once again:smile::smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook