What does descartes' rule of signs tell you about the possible number of positive real zeros and the possible number of negative real zeros of the function?
f(x)=3x^5-3x^2+x-4

the possible number of positive real zeros is
what? the possible number of negative real zeros is
what?

Step-by-step explanation:

The signs of the coefficients of the given terms are ...

  +  -  +  -

There are three sign changes, so the number of positive real zeros is 3 or 1.

When odd-degree terms have their signs changed, the signs become ...

  -  -  -  -

There are no sign changes, hence no negative real zeros.

_____

A graph confirms this evaluation.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: