What are all the possible rational zeros for #f(x)=x^4-7x^2+10# and how do you find all zeros?
1 Answer
Nov 20, 2016
Explanation:
Given:
#f(x) = x^4-7x^2+10#
By the rational root theorem, any rational zeros of
That means that the only possible rational zeros are:
#+-1, +-2, +-5, +-10#
However, note that we can factor
#x^4-7x^2+10 = (x^2-5)(x^2-2)#
#color(white)(x^4-7x^2+10) = (x^2-(sqrt(5))^2)(x^2-(sqrt(2))^2)#
#color(white)(x^4-7x^2+10) = (x-sqrt(5))(x+sqrt(5))(x-sqrt(2))(x+sqrt(2))#
So the only zeros of