How do you find all zeros of #f(x)=x^5+x^3-6x#?

1 Answer
Jan 12, 2017

Answer:

The zeros of #f(x)# are: #0, +-sqrt2, +-sqrt3 i#

Explanation:

#f(x) = x^5+x^3-6x#

The zeros of #f(x)# are the values of #x# where #f(x) = 0#

That is where: #x^5+x^3-6x =0#

#x(x^4+x^2-6) = 0#

Hence #x=0# or #x^4+x^2-6 =0#

Let #z=x^2#

#:. z^2 +z -6 =0#

#(z+3)(z-2)=0#

#-> z= 2 or -3#

#:. x=+-sqrt2 or +-sqrt3 i#

The zeros of #f(x)# are: #0, +-sqrt2, +-sqrt3 i#