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anonymous

  • one year ago

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?

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  1. anonymous
    • one year ago
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    HELP PLEASE

  2. anonymous
    • one year ago
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    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?

  3. anonymous
    • one year ago
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    yes

  4. anonymous
    • one year ago
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    Good. Now, are you able to simplify \(\sqrt{99}\) ?

  5. anonymous
    • one year ago
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    3√ 11

  6. anonymous
    • one year ago
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    right?

  7. anonymous
    • one year ago
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    Excellent. And do you know what \(\sqrt{-1}\) is?

  8. anonymous
    • one year ago
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    1

  9. anonymous
    • one year ago
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    No. The square root of -1 is the imaginary number i. It is referred to in the question. Have you seen it before?

  10. anonymous
    • one year ago
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    oh yes!

  11. anonymous
    • one year ago
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    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?

  12. anonymous
    • one year ago
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    a=-7 b=3√11

  13. anonymous
    • one year ago
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    Fantastic. Good job!

  14. anonymous
    • one year ago
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    Thank you sooo much :))))

  15. anonymous
    • one year ago
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    You're welcome.

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