SOLUTION: How many zeros are there in {{{F(X)=X^3-4X^2+2X+1}}}. Can you please show the work so i too can understand. Thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How many zeros are there in {{{F(X)=X^3-4X^2+2X+1}}}. Can you please show the work so i too can understand. Thank you       Log On


   

Question 38937: How many zeros are there in F%28X%29=X%5E3-4X%5E2%2B2X%2B1. Can you please show the work so i too can understand.
Thank you
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Well from
f(x) = x^3 - 4x^2 + 2x + 1
you can, by inspection, see that x = 1 is one of the zeroes, since f(1) = 0
Now if you factor f(x) you get
f(x) = (x - 1)(x^2 - 3x - 1)
The second polynomial is not factorable but the zeroes can be found using the quadratic formula, so that
x = 1 and
x = (3 ± sqrt(13)) / 2
Thus there are 3 zeroes,
one rational and two irrational...