1. determine whether -3 is a root of x3 + 3x2 + x + 1 = 0.
explain.

2. write a polynomial equation of least degree with
roots 3,-1, 2i, and -2i. how many times does the
graph of the related function intersect the x-axis?

1. The given equation does not have root at x = - 3.

2. (x - 3) (x + 1) (x² + 4) = 0

This curve will intersect twice the x-axis.

Step-by-step explanation:

1. If the right hand side of the equation  ......... (1) becomes same as the left hand side by putting x = - 3, then only we can conclude that x = - 3 is a root of the equation.

But in this case .

Therefore, x = - 3 is not a root of the above equation (1).

2. The equation of the polynomial with roots 3, -1, 2i, and -2i is

(x - 3) (x + 1) (x - 2i) (x + 2i) = 0

⇒ (x - 3) (x + 1) (x² + 4) = 0 (Answer)

Therefore, the graph of the above curve will intersect twice the x-axis in a real coordinate plane, at x = 3 and at x = -1. (Answer)

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

the final price would be 29.6925

step-by-step explanation:

39.59 minus 25% equals 29.6925