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Sum of roots, product of roots

  1. Jul 5, 2008 #1
    Hi, roots problem again x(.
    The roots of the equation x2 +px + 1 = 0 are a and b. If one of the roots of the equation x2 + qx + 1 = 0 is a3, prove that the other root is b3. [Done]

    Without solving any equation, show that q = p(p2 - 3). Obtain the quadratic equation with roots a9 and b9, giving the coefficients of x in terms of q.

    Can't solve the last one, which is a9 and b9. I got
    x2 + (q3 -3p)x + 1.
    it's suppose to be x^2 + [q2(q -3)]x + 1.
  2. jcsd
  3. Jul 8, 2008 #2


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    Homework Helper

    You don't mention it, but had you gotten the proof for [tex]q = p(p^2 - 3) [/tex] ? (It is pretty neat!)

    I think you can just argue by analogy for the last proposition. [tex]a^9 = (a^3)^3[/tex], and similarly for [tex]b^9[/tex], so the linear coefficient -- call it 's' -- for that last quadratic equation ought to be

    [tex]s = q(q^2 - 3)[/tex]

    (Is there a typo in your last line?)
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