Question

What are the zeros of the function f(x) = x4 – 4x² –5?

Answer 1

`x =i\\\\x =-i\\\\x=\sqrt 5\\\\x=-\sqrt 5`

Explanation:

`~~~~~~~~x^4-4x^2 -5 = 0\\\\\implies x^4-5x^2+x^2 -5 = 0\\ \\\implies x^2(x^2 -5)+(x^2-5) =0\\ \\\implies (x^2 +1)(x^2 -5) - 0\\\\\implies x^2+1 = 0~~~~~~~~~ \text{Or}~~~~~~~~~ x^2 -5 = 0\\\\\implies x^2 = -1~~~~~~~~~~~~ \text{Or}~~~~~~~~~x^2 = 5\\\\\implies x= \pm√(-1)~~~~~~~~~\text{Or}~~~~~~~~~x=\pm\sqrt 5\\\\\implies x = \pm i~~~~~~~~~~~~~~\text{Or}~~~~~~~~~x=\pm\sqrt 5\\`