anonymous
  • anonymous
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 5, -3, and -1 + 2i
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
sorry it went away
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
before we begin is it clear that two factors are \((x-5)\) and \((x+3)\)?

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anonymous
  • anonymous
yes
anonymous
  • anonymous
ok so the real job (before multiplying out) is the find the quadratic polynoimial with zeros at \(-1+2i\) and its conjugate \(-1-2i\)
anonymous
  • anonymous
you want the easy way, or the real real easy way?
anonymous
  • anonymous
real real easy
anonymous
  • anonymous
ok actually lets to the easy way first then the real real easy way
anonymous
  • anonymous
we can work backwards starting with \[x=-1+2i\] add 1 and get \[x+1=2i\] then square (carefully) to get \[(x+1)^2=(-2i)^2\] or \[x^2+2x+1=-4\]
anonymous
  • anonymous
add 4 to both sides and get \[x^2+2x+5=0\] and that is your polynomial
anonymous
  • anonymous
the real real easy way requires memorizing something that if \(a+bi\) is a zero of a quadratic, then it is \[x^2-2ax+(a^2+b^2)\] so in your case \(a=-1,b=2\) and the quadratic is \[x^2-2\times (-1)x+(-1)^2+2^2\] i.e. \[x^2+2x+5\]
anonymous
  • anonymous
those arent any options tho :(
anonymous
  • anonymous
your final job is to multiply \[(x-5)(x+3)(x^2+2x+5)\]
anonymous
  • anonymous
if it was me, i would cheat so as not to screw up the algebra when multiplying
anonymous
  • anonymous
you know how to do that?
anonymous
  • anonymous
wait let me try again
anonymous
  • anonymous
ok i will leave you to it, then show you how to get the answer for sure
anonymous
  • anonymous
yeah the answer i get does not match up with my choices
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=%28x-5%29%28x%2B3%29%28x^2%2B2x%2B5%29
anonymous
  • anonymous
see if that one does
anonymous
  • anonymous
Oh thank-you! maybe i was multiplying something wrong!
anonymous
  • anonymous
that is why i said "cheat" is is easy to make a mistake when multiplying all this muck out
anonymous
  • anonymous
yw

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