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Darina [25.2K]
2 years ago
7

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

Mathematics
1 answer:
vaieri [72.5K]2 years ago
7 0

Answer:

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

Step-by-step 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\sqrt{-1}~~~~~~~\text{or}~~~~~~~~~~ x = \pm\sqrt 2\\\\\implies x= \pm i~~~~~~~~~~~~~\text{or}~~~~~~~~~ x= \pm\sqrt 2

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