3x^4 + 5x^2 - 2 = 0

Question

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?

Answer 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