What are all the possible rational zeros for #f(x)=4x^3-9x^2+6x-1# and how do you find all zeros?
1 Answer
Feb 19, 2017
Explanation:
Given:
#f(x) = 4x^3-9x^2+6x-1#
By the rational roots theorem, any rational zeros of
That means that the only possible rational zeros are:
#+-1/4, +-1/2, +-1#
Here's a non-standard way of finding the zeros:
I notice that the coefficients are all fairly small and the signs alternate.
Taking them in reverse order and stringing them together we get:
#1694 = 2*7*11*11 = 14*11*11#
Hence we find:
#t^3+6t^2+9t+4 = (t+4)(t+1)(t+1)#
Then putting
#4x^3-9x^2+6x-1 = (4x-1)(x-1)(x-1)#
So