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    f(x)=2x^3-5x^2+px-5, p E R

    given that 1-2i and 1+2i are complex solutions of f(x)=0

    Solve f(x)=0 and find p

    what are you suppose to do?
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    multiply out (x-(1-2i))(x-(1+2i))
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    (Original post by PeeWeeDan)
    multiply out (x-(1-2i))(x-(1+2i))
    why? where did you get that from? why x- the roots?
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    Hmm, ok: are you aware of the relationship between the roots of a polynomial and the polynomial's coefficients?

    It is: suppose we have a polynomial ax^3 + bx^2 + cx + d with zeros \alpha, \beta, \gamma, then we have:
    \dfrac{-b}{a} = \alpha + \beta + \gamma;

    \dfrac{c}{a} = \alpha \beta + \alpha \gamma + \beta \gamma;

    \dfrac{-d}{a} = \alpha \beta \gamma

    So, can you use this to find our third root, \gamma (say)?

    Spoiler:
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    We have that (1-2i) + (1+2i) + \gamma = 5/2 by one of the relations above.


    Now we have our roots, we can easily compute p.
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    (Original post by emmaxoxo)
    why? where did you get that from? why x- the roots?
    Because the equation will factorize to form (ax-b)(x-(1-2i))(x-(1+2i))=0 where the third solution is x=b/a.

    Just for reference the answer I get without writing anything down(so pinch of salt please) is p=12 and x=1/2... but I'm not 100% would need to check it.
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    (Original post by PeeWeeDan)
    Because the equation will factorize to form (ax-b)(x-(1-2i))(x-(1+2i))=0 where the third solution is x=b/a.

    Just for reference the answer I get without writing anything down(so pinch of salt please) is p=12 and x=1/2... but I'm not 100% would need to check it.
    Yes, there the right answers.

    so far i have x^2-2x+5, now what do I do?
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    (Original post by emmaxoxo)
    Yes, there the right answers.

    so far i have x^2-2x+5, now what do I do?
    (ax-b)(x^2-2x+5)= whatever that first polynomial was.

    Solve.
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    (Original post by PeeWeeDan)
    (ax-b)(x^2-2x+5)= whatever that first polynomial was.

    Solve.
    Yep done that got x=1/2, but where do you get p=12, i know it's 10+2 from answers, but where have those numbers come from?
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    (Original post by emmaxoxo)
    Yep done that got x=1/2, but where do you get p=12, i know it's 10+2 from answers, but where have those numbers come from?
    By multiplying out the brackets and having a look at the equation.
 
 
 
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