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Math Help - One root of a poly. equation is i. What are the other three?

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    One root of a poly. equation is i. What are the other three?

    "One root of x^4 - 3x^2 - 4 = 0 is i. What are the other three roots?"

    How do I do this with i?

    If someone could briefly walk me through this, that'd be awesome. Thanks.
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  2. #2
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    Quote Originally Posted by Savior_Self View Post
    "One root of x^4 - 3x^2 - 4 = 0 is i. What are the other three roots?"

    How do I do this with i?

    If someone could briefly walk me through this, that'd be awesome. Thanks.
    Hi Savior_Self,

    Remember, if an imaginary number is a zero to the polynomial function, so is its conjugate.

    Therefore, if i is a zero, then -i is a zero.

    (x-i) and (x+i) are factors.

    Multiply these two together to get x^2+1

    Now, divide this into your original function to get x^2-4

    If i is a factor, and -i is a factor and x^2-4 is a factor then (x-i)(x+i)(x-2)(x+2)=0

    Your zeros are \{i, -i, 2, -2\}
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