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babydoll332

  • 2 years ago

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, -2, and -1 + 2i

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  1. babydoll332
    • 2 years ago
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    f(x) = x4 - 3x3 + 8x2 + 13x + 40 correct

  2. satellite73
    • 2 years ago
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    start with \[(x-4)(x+2)(x-(-1+2i))(x-(1-2i))\] and multiply out but before we being the last product is very easy

  3. babydoll332
    • 2 years ago
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    can you kinda go back words with me work best that way please and thanks

  4. satellite73
    • 2 years ago
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    if the zeros are \(a+bi\) and \(a-bi\) the quadratic is \[x^2-2ax+(a^2+b^2)\] in your case it is \[x^2+2x+5\]

  5. satellite73
    • 2 years ago
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    ok lets start at the very beginning

  6. satellite73
    • 2 years ago
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    if \(-1+2i\) is a zero, then so is its conjugate \(-1-2i\)

  7. satellite73
    • 2 years ago
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    the quadratic equation that will have those two zeros is \[x^2+2x+5\] is it clear how i got that?

  8. babydoll332
    • 2 years ago
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    rightt i got that

  9. satellite73
    • 2 years ago
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    oh ok good then your final job is to multiply out \[(x-4)(x+2)(x^2+2x+5)\]

  10. babydoll332
    • 2 years ago
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    f(x) = x4 - 7x2 - 26x - 40

  11. satellite73
    • 2 years ago
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    you can do it in any order you like , but as you can see it is a bunch of algebra you have to do. yes, that is correct

  12. babydoll332
    • 2 years ago
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    thankkkksss

  13. satellite73
    • 2 years ago
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    yw, it looks like you did it on your own good job

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