What are all the possible rational zeros for #f(x)=x^3-13x^2+23x-11# and how do you find all zeros?
1 Answer
The "possible" rational zeros are:
The actual zeros are:
Explanation:
#f(x) = x^3-13x^2+23x-11#
By the rational roots theorem, any rational zeros of
That means that the only possible rational zeros are:
#+-1, +-11#
Note that the sum of the coefficients of
#1-13+23-11 = 0#
Hence
#x^3-13x^2+23x-11 = (x-1)(x^2-12x+11)#
The sum of the coefficients of the remaining quadratic is zero too:
#1-12+11 = 0#
So
#(x^2-12x+11) = (x-1)(x-11)#
So the zeros of