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Math Help - Roots of a polynominalp(x)

  1. #1
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    Roots of a polynominalp(x)

    Hey, I was wondering if anybody would be able to explain how to arrive to (a). It's in my notes but I don't seem how they got there?

    Find the roots of the following polynominal.

    p(x) = x^4 - x^3 + 4x^2 + 3x + 5

    Info: b = 1 + 2i is a root.

    Sp b(bar) = 1-2i should also be a root.

    Try to divide p(x) by (x-(1+2i)) (x-(1-2i))
    (a) = x^2 - 2x +5


    Thanks :]
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  2. #2
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    Quote Originally Posted by schrei View Post
    Hey, I was wondering if anybody would be able to explain how to arrive to (a). It's in my notes but I don't seem how they got there?

    Find the roots of the following polynominal.

    p(x) = x^4 - x^3 + 4x^2 + 3x + 5

    Info: b = 1 + 2i is a root.

    Sp b(bar) = 1-2i should also be a root.

    Try to divide p(x) by (x-(1+2i)) (x-(1-2i))
    (a) = x^2 - 2x +5
    Multiply out the outer brackets: (x-(1+2i)) (x-(1-2i)) = x^2 -(1+2i+1-2i)x + (1+2i)(1-2i) = x^2 - 2x + (1+2i)(1-2i)<br />
. Now multiply out the remaining brackets and you should see the required result.
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  3. #3
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    Just a little simpler, I think.

    (x-(1+2i)) (x-(1-2i))= [(x-1)+ 2i][(x-1)- 2i], a product of "sum and difference". Their product, then, is (x-1)^2- (2i)^2= x^2- 2x+ 1+ 4= x^2- 2x+ 5.
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