Find all the zeros of the equation 3x^2-4=x^4

  x = (±√7 ±i)/2

Step-by-step explanation:

The equation can be rewritten to look like a quadratic in x². In standard form, it is ...

  (x²)² -3x² +4 = 0

Then by the quadratic formula, ...

  x² = (-(-3) ± √((-3)²-4(1)(4)))/(2(1)) = (3 ± √-7)/2

  x = ±√((3 ±i√7)/2)

This can be simplified to ...

  x = ±(√7)/2 ±i/2

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Comment on simplification

The method I used was a combination of numerical technique and guessing. The value of x has a rational imaginary part, so we guessed that the real part was a simple square root. That guess turned out to be accurate.