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Math Help - Imaginary Coefficients

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    Imaginary Coefficients

    Find a possible polynomial p(x) such that the degree of p(x) is 3 and all of the coefficients are imaginary.
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  2. #2
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    Quote Originally Posted by SHiFT View Post
    Find a possible polynomial p(x) such that the degree of p(x) is 3 and all of the coefficients are imaginary.
    imaginary coefficients? first I've heard of a problem like this.

    how about ...

    p(x) = ix^3 + 2ix^2 + 3ix + 4i = i(x^3 + 2x^2  + 3x + 4)
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    Sorry, I also forgot to include that in the directions it says let p(x) be a polynomial such that p(-1)=0 and p(3)=0
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    Quote Originally Posted by SHiFT View Post
    Sorry, I also forgot to include that in the directions it says let p(x) be a polynomial such that p(-1)=0 and p(3)=0
    Just a minor detail, right?

    Okay that means that x+1 and x- 3 must be factors: write the polynomial as [tex](ax+ b)(x+1)(x-3)= (ax+b)(x^2- 2x+ 1)= ax^3+ (b-2a)x^2+ (a-2b)x+ b[/quote]. Now choose a and b to be imaginary number such that neither b-2a nor a-2b is 0. a= b= i works nicely.
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