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Algebra

Find all the zeros of the equation.

-3x^4+27x^2+1200=0

I know the zeros are –5, 5, –4i, and 4i, but how do I get there?

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  1. - 3 x⁴ + 27 x² + 1200 = 0

    - 3 ( x⁴ - 9 x² - 400 ) = 0

    Divide both sides by - 3

    x⁴ - 9 x² - 400 = 0

    ( x⁴ - 25 x² ) + ( 16 x² - 400 ) =

    x² ( x² - 25 ) + 16 ( x² - 25 ) =

    ( x² - 25 ) ( x² + 16 ) =

    ( x + 5 ) ( x - 5 ) ( x² + 16 ) = 0

    The equation will be equal to zero when the expressions in parentheses are equal to zero.

    This means that you have three conditions.

    First condition:

    x + 5 = 0

    Subtract 5 to both sides

    x = - 5

    Second conditiion:

    x - 5 = 0

    Add 5 to both sides

    x = 5

    Third condition:

    x² + 16 = 0

    Subtract 16 to both sides

    x² = - 16

    x = ± √ - 16

    x = ± 4 i

    So the solutions are:

    x = - 5 , x = 5 , x = 4 i , x = 4 i

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  2. Thank you!

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