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!

Polynomial Functions

  1. Jun 19, 2004 #1
    Could someone please help me with this question, I'd be most obliged:

    Q) Find the value of "a" for which the function
    2x^3 - ax^2 - 12x - 7
    has a repeated factor.

    Thanks
     
  2. jcsd
  3. Jun 19, 2004 #2

    Gokul43201

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If you mean two identical roots, then ...

    write [tex] 2x^3 - ax^2 - 12x - 7 = (x-b)^2(2x-c) [/tex]

    Expand the RHS and compare coefficients. You have 3 equations in 3 unknowns.
     
  4. Jul 4, 2004 #3
    Since we are seeking only a specific solution, we can keep in mind that if the cubic has a double root, that this root is also present in its derative. The derative is: 2(3X^2-aX-6). Here if we let a =3, we get X =2, -1. -1 works in the original equation and the factoring then is 2(x+l)^2(x-7/2).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook