Question

What are the zeros of the function f(x) = x^4 - x² - 2?

Answer 1

`x= i\\\\ x = -i \\\\x=\sqrt 2\\\\x = -\sqrt 2`

Explanation:

`~~~~~~x^4 -x^2 -2=0\\\\\implies x^2 \cdot x^2-2x^2 +x^2 -2 = 0\\\\\implies x^2(x^2 -2) +(x^2 -2) =0\\\\\implies (x^2 +1)(x^2 -2) = 0\\\\ \implies x^2 +1=0~~~~~~~~\text{or}~~~~~~~~~x^2 -2 = 0\\\\ \implies x = \pm√(-1)~~~~~~~\text{or}~~~~~~~~~~ x = \pm\sqrt 2\\\\\implies x= \pm i~~~~~~~~~~~~~\text{or}~~~~~~~~~ x= \pm\sqrt 2`