Question

Find all the zeros of the equation

Answer 1

Rearrange the formula as

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

Define
`t=x^2` so that the equation becomes a quadratic one:

`t^2+3t-4=0`

Use the quadratic formula to solve this:

`t_(1,2) = (-3\pm√(9+16))/(2) = (-3\pm 5)/(2)`

Which implies

`t=(-3-5)/(2) =-4 \text{ or } t = (-3+5)/(2) = 1`

Now, remember that
`t=x^2`

So, the solutions in t translate as

`t=-4 \implies x^2=-4 \iff x=\pm 2i,\quad t=1 \implies x^2=1 \iff x=\pm 1`