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Math Help - Help with solving for x.

  1. #1
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    Help with solving for x.

    x^4 - 7 = 6x^2

    I get this far:

    x^4 - 7 = 6x^2
    x^4 + 0x^3 - 6x^2 + 0x - 7 = 0

    Factors of -7:
    +/- 1, +/- 7

    I don't know where to go from this point.

    The homework relates to solving polynomial equations using factor/remainder theorem. Can someone please help?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Jeavus View Post
    x^4 - 7 = 6x^2

    I get this far:

    x^4 - 7 = 6x^2
    x^4 + 0x^3 - 6x^2 + 0x - 7 = 0

    Factors of -7:
    +/- 1, +/- 7

    I don't know where to go from this point.

    The homework relates to solving polynomial equations using factor/remainder theorem. Can someone please help?
    the factor theorem is not needed here

    bring everything to one side:

    x^4 - 6x^2 - 7 = 0

    \Rightarrow \left( x^2 \right)^2 - 6 \left( x^2 \right) - 7 = 0

    this is a quadratic in x^2, it can be factored
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  3. #3
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    How can that be factored?

    Ahh...alright. Let's see.

    (x^2)^2 - 6(x^2) - 7 = 0
    (x^2 - 7)(x^2+1) = 0

    Is this correct?

    How would I continue?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Jeavus View Post
    How can that be factored?

    Ahh...alright. Let's see.

    (x^2)^2 - 6(x^2) - 7 = 0
    (x^2 - 7)(x^2+1) = 0

    Is this correct?

    How would I continue?
    how would you continue if it was a regular quadratic?
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