algebra

3x^4 + 5x^2 - 2 = 0
give imaginary and real roots
rational roots theorem factors of (+-)p/q are possible rational zeros of function f where the coefficients of f are integers.

how do you go about solving this?

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  1. let y = x2, so

    so 3x^4 + 5x^2 - 2 = 0 ---> 3y^2 + 5y - 2 = 0
    (3y - 1)(y + 2) = 0
    y = 1/3 or y = -2
    so
    x^2 = 1/2 OR x^2 = -2
    x = ±1/√2 or x = ± i√2

    can be shortened if you can see that
    3x^4 + 5x^2 - 2 = 0 ---> (3x^2 - 1)(x^2 + 2) = 0
    etc

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