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: Real find both roots of the equation

  1. Oct 14, 2005 #1


    User Avatar

    x^2 +6x +k=0 has one root (a) where Im (a) =2, If k is real find both roots of the equation and k

    So i got b+ 2i is the root

    (b+2i)^2 +6(x+2i) +k=0
    and after expanding it out, i have no clue what to do. Please help. THanks
  2. jcsd
  3. Oct 14, 2005 #2
    Try using the quadratic formula and thinking about what comes underneath the square root in relation to Im(a) = 2
  4. Oct 14, 2005 #3


    User Avatar
    Science Advisor
    Homework Helper

    You know that if the roots are complex then the two roots are complex conjugates of each other. The sum of the roots is -6 (negative ratio of linear coefficient to quadratic coefficient) so you should be able figure out what what the real part has to be. Once you have a root you can find k.
  5. Oct 15, 2005 #4


    User Avatar
    Science Advisor

    I wish you had shown us what you got by expanding it! Clearly that "6(x+ 2i)" should be "6(b+ 2i)" but I don't know whether that's a typo or you actually left the x in your calculation.
    Expand it out and set it equal to 0. For a complex number to be equal to 0, both real and imaginary parts must be 0. That gives you two (simple) equations for the two (real) unknown numbers, b and k.
  6. Nov 1, 2006 #5
    sorry for bumping this topic

    but could anyone please explain in detail how this question is done?
  7. Nov 1, 2006 #6


    User Avatar
    Science Advisor

    First try doing it yourself! You said "after expanding it out, i have no clue what to do." and I asked you to show what you got after expanding. You should get a complex number depending on b and k. As I said before, set real and imaginary parts equal to 0 and you get two equations for b and k. Solve those equations.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook