anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
f(x) = x4 - 3x3 + 8x2 + 13x + 40 correct
anonymous
  • anonymous
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
anonymous
  • anonymous
can you kinda go back words with me work best that way please and thanks

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anonymous
  • anonymous
if the zeros are \(a+bi\) and \(a-bi\) the quadratic is \[x^2-2ax+(a^2+b^2)\] in your case it is \[x^2+2x+5\]
anonymous
  • anonymous
ok lets start at the very beginning
anonymous
  • anonymous
if \(-1+2i\) is a zero, then so is its conjugate \(-1-2i\)
anonymous
  • anonymous
the quadratic equation that will have those two zeros is \[x^2+2x+5\] is it clear how i got that?
anonymous
  • anonymous
rightt i got that
anonymous
  • anonymous
oh ok good then your final job is to multiply out \[(x-4)(x+2)(x^2+2x+5)\]
anonymous
  • anonymous
f(x) = x4 - 7x2 - 26x - 40
anonymous
  • anonymous
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
anonymous
  • anonymous
thankkkksss
anonymous
  • anonymous
yw, it looks like you did it on your own good job

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