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 here are my choices f(x) = x^4 - 7x^2 - 26x - 40 f(x) = x^4 - 3x^3 - 8x^2 - 13x - 40 f(x) = x^4 + 6.5x^2 - 26x - 40 f(x) = x^4 - 3x^3 + 8x^2 + 13x + 40
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
this again ready?
anonymous
  • anonymous
i dont know how to do this at all lolol
anonymous
  • anonymous
ok then we better go slow

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More answers

anonymous
  • anonymous
do you know if \(r\) is a zero, then one factor must be \((x-r)\)? so in this case you have \(4\) is a zero making one factor \((x-4)\)
anonymous
  • anonymous
clear or not? that is really what we need to start this
anonymous
  • anonymous
oh okay so (x-4) and (x+2) ?
anonymous
  • anonymous
right
anonymous
  • anonymous
we start with \[(x-4)(x+2)\] now we have more work to do
anonymous
  • anonymous
you also need the quadratic that has the zeros of \(-1+2i\) and it "conjugate" \(-1-2i\) next job is to find that
anonymous
  • anonymous
any ideas? "no" is a fine answer
anonymous
  • anonymous
no i dont know
anonymous
  • anonymous
ok there is a hard way, an easy way, and a really really easy way lets do the easy way first, then the real easy way
anonymous
  • anonymous
work backwards starting with \[x=-1+2i\] add \(1\) to get \[x+1=2i\]
anonymous
  • anonymous
then square both sides (carefully) to get \[(x+1)^2=(2i)^2\] or \[x^2+2x+1=-4\]
anonymous
  • anonymous
add 4 to both sides to finish with \[x^2+2x+5\]
anonymous
  • anonymous
final job is to multiply \[(x-4)(x+2)(x^2+2x+5)\]i would cheat so as not to screw up the algebra
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=%28x-4%29%28x%2B2%29%28x^2%2B2x%2B5%29
anonymous
  • anonymous
and would that be the answer? or is there more
anonymous
  • anonymous
OOO got it. thank you
anonymous
  • anonymous
yeah that is it
anonymous
  • anonymous
yw

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