anonymous
  • anonymous
A student uses the quadratic formula to solve a quadratic equation and determines that one of the solutions is x equals negative seven plus square root of negative 99 end square root. What are the values of a and b if this solution is written in the form x = a + bi, where a and b are real numbers?
Mathematics
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anonymous
  • anonymous
A student uses the quadratic formula to solve a quadratic equation and determines that one of the solutions is x equals negative seven plus square root of negative 99 end square root. What are the values of a and b if this solution is written in the form x = a + bi, where a and b are real numbers?
Mathematics
jamiebookeater
  • jamiebookeater
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
HELP PLEASE
anonymous
  • anonymous
Bit of factoring is all that's required. You are given\[x=-7 + \sqrt{-99}\]Let's do some factoring using the rules of working with radicals.\[x=-7 + \sqrt{99}\sqrt{-1}\]You OK with that so far?
anonymous
  • anonymous
yes

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anonymous
  • anonymous
Good. Now, are you able to simplify \(\sqrt{99}\) ?
anonymous
  • anonymous
3√ 11
anonymous
  • anonymous
right?
anonymous
  • anonymous
Excellent. And do you know what \(\sqrt{-1}\) is?
anonymous
  • anonymous
1
anonymous
  • anonymous
No. The square root of -1 is the imaginary number i. It is referred to in the question. Have you seen it before?
anonymous
  • anonymous
oh yes!
anonymous
  • anonymous
OK. So now your question looks like\[x=-7 + \sqrt{99}\sqrt{-1}\]\[x=-7+3\sqrt{11}i\]Compare this with\[x=a+bi\]What are the values of a and b?
anonymous
  • anonymous
a=-7 b=3√11
anonymous
  • anonymous
Fantastic. Good job!
anonymous
  • anonymous
Thank you sooo much :))))
anonymous
  • anonymous
You're welcome.

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