Roots of Polynominals

Maths and statistics discussion, revision, exam and homework help.

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  1. pleasedtobeatyou's Avatar
    • Respected Member
    • Posts: 220
    Roots of Polynominals
    z^2 + (p+5i)z + (2-i)q = 0



One root is (1+2i)



Therefore: Alpha+Beta=(-p-5i), AlphaBeta=(2-i)q

    How would I find p and q? It seems impossible to form any equation without p and q
    Last edited by pleasedtobeatyou; 15-06-2012 at 22:00.
  2. ghostwalker's Avatar
    • Outcast of Imrryr
    • Location: CA13
    Re: Roots of Polynominals
    (Original post by pleasedtobeatyou)
    z^2 + (p+5i)z + (2-i)q = 0



One root is (1+2i)



Therefore: Alpha+Beta=(-p-5i), AlphaBeta=(2-i)q

    How would I find p and q? It seems impossible to form any equation without p and q
    I presume p,q are real.

    It's just a case of following your nose.

    One root's given.

    Sum of roots gives you the second root in terms of p.

    Sub into the product of roots and equate real/imaginary part.

    Edit: Or as BabyMaths suggested below; probably easier.
    Last edited by ghostwalker; 15-06-2012 at 22:05. Reason: Grammar
  3. BabyMaths's Avatar
    • Peer Of The TSR Realm
    • Posts: 1,566
    Re: Roots of Polynominals
    Sub in 1+2i. Consider real and imaginary parts.
  4. pleasedtobeatyou's Avatar
    • Respected Member
    • Posts: 220
    Re: Roots of Polynominals
    Ahh indeed

    Thanks for the quick response guys
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