# 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