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Math Help - imaginary numbers....

  1. #1
    Member Veronica1999's Avatar
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    imaginary numbers....

    Which one of the following statements is not true for the equation ix(squared) - x + 2i =0 where i = root -1?

    a. the sum of the roots is 2
    b. the discriminant is 9
    c. the roots are imaginary
    d. the roots can be found by using the quadratic formula
    e. the roots can be found by factoring, using imaginary numbers

    I guessed the answer is a because the sum of the roots should be -1/i.
    What is i? I don't understand the problem at all.
    Does i stand for imaginary numbers?
    When do I use imaginary numbers?
    Last edited by Veronica1999; June 26th 2010 at 11:26 AM.
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  2. #2
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    Quote Originally Posted by Veronica1999 View Post
    Which one of the following statements is not true for the equation ix(squared) - x + 2i =0 where i = root -1?

    a. the sum of the roots is 2
    b. the discriminant is 9
    c. the roots are imaginary
    d. the roots can be found by using the quadratic formula
    e. the roots can be found by factoring, using imaginary numbers

    I guessed the answer is a because the sum of the roots should be -1/i.
    What is i? I don't understand the problem at all.
    Does i stand for imaginary numbers?
    When do I use imaginary numbers?
    You are told in the question itself what i is. If you have never learned about imaginary numbers, I'm not sure why you are attempting a question like this.

    The given equation can be re-written (by dividing both sides by i) as [tex]x^2 + ix + 2 = 0 (note that 1/i = -i ....).

    If you now apply the quadratic formula to this you get x = i or x = -2i ....
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  3. #3
    Member Veronica1999's Avatar
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    Quote Originally Posted by mr fantastic View Post
    You are told in the question itself what i is. If you have never learned about imaginary numbers, I'm not sure why you are attempting a question like this.

    The given equation can be re-written (by dividing both sides by i) as [tex]x^2 + ix + 2 = 0 (note that 1/i = -i ....).

    If you now apply the quadratic formula to this you get x = i or x = -2i ....
    Now I understand why c d and e are true.
    I was just curious how a negative number could be in a square root.
    At first it didn't make sense, but google helped a lot.
    I am still not sure why b is true.
    Can you show me?
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  4. #4
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    Quote Originally Posted by Veronica1999 View Post
    Now I understand why c d and e are true.
    I was just curious how a negative number could be in a square root.
    At first it didn't make sense, but google helped a lot.
    I am still not sure why b is true.
    Can you show me?
    Looking at the original equation

    i\,x^2 - x + 2i = 0

    you have a = i, b = -1, c = 2i.


    So \Delta = b^2 - 4ac

     = (-1)^2 - 4(i)(2i)

     = 1 - 8i^2

     = 1 + 8

     = 9.
    Last edited by mr fantastic; June 26th 2010 at 09:34 PM.
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