How do you find all the zeros of #F(x) = x^4 - 13x^2 + 36#?

1 Answer
Jul 16, 2016

Answer:

Zeros: #+-3#, #+-2#

Explanation:

Since there are no terms of odd degree, we can treat this as a quadratic in #x^2# to simplify it, then factorize each of the resulting quadratic factors.

First note that #36 = 9xx4# and #9+4=13#, so we find:

#x^4-13x^2+36#

#=(x^2)^2-13(x^2)+36#

#=(x^2-9)(x^2-4)#

#=(x^2-3^2)(x^2-2^2)#

#=(x-3)(x+3)(x-2)(x+2)#

Hence zeros:

#+-3#, #+-2#