Question

Help me fully understand Fundamental Theorem of Algebra, using this example: Find all the real zeros in the function: f(x) Xcubed-6Xsquared+11x-6

Answer 1

Using fundamental theorem of algebra?! lol

Answer 2

It just tells you that there are 3 roots.

Answer 3

The highest degree is \(3\) because of \(x^3\)

Answer 4

holy crud. FIND ALL THE REAL ZEROS IN THE FUNCTION. i know the roots and degree

Answer 5

If a polynomial function has integer coefficients, then every rational zero will have the form (p)/(q) where p is a factor of the constant and q is a factor of the leading coefficient.
p=6
q=1

possible zeros
\[\pm1,\pm2,\pm3,\pm6\]
you can substitute
them one at a time
substituting 1
(1)^3 - 6(1)^2 + 11(1) - 6 = 0

this checks so x=1 or x-1 = 0
we can divide x-1 into the equation:

we get x^2 - 5x + 6 factoring we get
(x-2)(x-3)
so----- > (x-1)(x-2)(x-3)

so 1,2,3 are real zeros