anonymous
  • anonymous
One solution to a quadratic equation is x equals start fraction negative nine plus 21 i over three end fraction full stop What is the solution in simplified standard form, x = a + bi, if a and b are real numbers? Help please
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Mertsj
  • Mertsj
\[\frac{-9+21i}{3}=\frac{-9}{3}+\frac{21i}{3}=-3+7i\]
anonymous
  • anonymous
Thank you bunches. :) Can you help me with 2 more?
Mertsj
  • Mertsj
Possibly

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anonymous
  • anonymous
The complex solution to a quadratic equation is x equals start fraction negative four plus or minus square root of negative 80 end square root over four end fraction full stop Write this solution in standard form, x = a ± bi, where a and b are real numbers.
anonymous
  • anonymous
\[x=\frac{-4\pm\sqrt{-80}}{4}\]?
anonymous
  • anonymous
yes
anonymous
  • anonymous
ok we look for the largest perfect square that is a factor of 80 i get 16 because \(80=16\times 5\)
anonymous
  • anonymous
okay that makes sense
anonymous
  • anonymous
therefore \[\sqrt{-80}=\sqrt{16\times 5\times (-1)}=4\sqrt{5}i\]
anonymous
  • anonymous
woah you lost me D: lol
anonymous
  • anonymous
i guess i skipped a step \[\sqrt{16\times 5\times (-1)}=\sqrt{16}\sqrt{5}\sqrt{-1}=4\sqrt{5}i\]
anonymous
  • anonymous
since \(\sqrt{16}=4\) and \(\sqrt{-1}\) gets written as \(i\)
anonymous
  • anonymous
that is why we were looking for the largest perfect square that is a factor of 80
anonymous
  • anonymous
let me know when we can continue, it is not over yet
anonymous
  • anonymous
okay that makes sense
anonymous
  • anonymous
that was the hard part though now we have \[\frac{-4\pm4\sqrt{5}i}{4}\]divide each part of the numerator by \(4\) and you are done
anonymous
  • anonymous
this is what you have to do for all of them write the radical in simplest radical form for example since \(25\times2=50\) you would have \[\sqrt{-50}=5\sqrt{2}i\]
anonymous
  • anonymous
The number root of order five of ninety one to the power of four end power can be written as ninety one to the power of start fraction cap a over cap b end fraction end power. What is the value of A?

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