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Thread: Polynomial

  1. #1
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    Polynomial

    If P(z) is a polynomial of degree 4 with all its coefficients real with ai, bi as two of the zeros, then tern that does not contain z is:

    can you guys please solve this i got no idea how to approach this

    thanks
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  2. #2
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    I'm not sure what you mean by "the term that does not contain z..."

    Since the coefficients are all real, complex solutions occur as conjugates, so assuming \displaystyle a \neq -b, that means \displaystyle -ai and \displaystyle -bi are also roots.

    Therefore \displaystyle P(z) = \alpha(z - ai)(z + ai)(z - bi)(z + bi).
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  3. #3
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    Quote Originally Posted by Barney View Post
    If P(z) is a polynomial of degree 4 with all its coefficients real with ai, bi as two of the zeros, then tern that does not contain z is:

    can you guys please solve this i got no idea how to approach this

    thanks
    Please post the question exactly as it's written in the source you got it from.
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  4. #4
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    Exactly as the question says, and it a multiple choice:
    If P(z) is a polynomial of degree 4 with all its coefficients real with ai, bi(a, b element R) as two of the zeros, then the term that does not contain z is:
    Answers:
    A) ab
    B) a-b
    C) a+b
    D) a^3b^3
    E) a^2b^2
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  5. #5
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    I think it's asking for the value of the constant term.

    Expand the expression I gave above...
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  6. #6
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    Quote Originally Posted by Barney View Post
    Exactly as the question says, and it a multiple choice:
    If P(z) is a polynomial of degree 4 with all its coefficients real with ai, bi(a, b element R) as two of the zeros, then the term that does not contain z is:
    Answers:
    A) ab
    B) a-b
    C) a+b
    D) a^3b^3
    E) a^2b^2
    Doesn't the problem also say that the polynomial is "monic" (coefficient of highest power is 1)? If the polynomial were not monic, none of those would be true.
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