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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.

  2. jcsd
  3. Jun 19, 2004 #2


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    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).
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