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Math Help - linear and quadratic polynomials

  1. #1
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    Post linear and quadratic polynomials

    Need help with this one please, The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients. my answer is f(x) = (x-3)(x^2-8x+16) thanks for checking. would like to make sure.
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  2. #2
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    Quote Originally Posted by wayne View Post
    Need help with this one please, The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients. my answer is f(x) = (x-3)(x^2-8x+16) thanks for checking. would like to make sure.
    Hello,

    - if x = -3 is a solution then the corresponding linear factor is (x+3)

    - if x = 4i is a solution then x = -4i is a solution too. Otherwise you will get an equation containing imaginary numbers. The linear factors are now (x-4i) and (x+4i).

    - f(x) = (x+3)(x-4i)(x+4i) = (x+3)(x^2+16)
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  3. #3
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    Smile thank you

    thanks for checking my answer.
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