How do you find the number of roots for #f(x) = 2x^3 – 12x^2 + 11x + 2# using the fundamental theorem of algebra?
1 Answer
The fundamental theorem of algebra tells us that this cubic has
We can further discover that all
Explanation:
The fundamental theorem of algebra (FTOA) tells us that any polynomial of degree
A straightforward corollary of that, often stated as part of the FTOA is that a polynomial of degree
This follows since given a polynomial of degree
In our example,
We can find out more by examining the discriminant
#Delta = b^2c^2-4ac^3-4b^3d-27a^2d^2+18abcd#
In our example,
#Delta = 17424-10648+13824-432-9504 = 10664#
Since
Using Descartes's Rule of Signs we can also tell that