# How do you find the number of roots for #f(x) = 3x^4 + x + 2# using the fundamental theorem of algebra?

##### 1 Answer

By the FTOA,

Further we find that none are Real.

#### Explanation:

The fundamental theorem of algebra (FTOA) tells us that any polynomial in one variable of degree

A straightforward corollary of this, often stated as part of the FTOA is that a polynomial of degree

In our example:

#f(x) = 3x^4+x+2#

is of degree

What else can we find out about these zeros?

The pattern of signs of the coefficients of

The pattern of signs of

Note that when

#f(x) > 0#

When

Hence:

#f(x) > 0#

So