Question

Graph and investigate a polynomial with the followingfeatures:6th degree2 double root*Negative orientation* It can have other roots but must have only twodouble roots

Answer 1

We are asked to write a polynomial with the following characteristics:

1. 6th degree, this means that the maximum exponent must be 6

2. two double roots, this means it must contain two elements of the form:

`(x-a)^2`

3. Negative orientation. This means that it must be multiplied by a constant k < 0.

Therefore, a polynomial with such characteristics could be:

`y=-(x-1)^2(x+1)^2(x+2)(x+3)`

The graph of this polynomial is the following:

According to the graph:

`x\rightarrow-\infty,y\rightarrow-\infty`

and

`x\rightarrow\infty,y\rightarrow-\infty`

It has degree 6 and the orientation is negative