Mathematics
Find all the zeros of the function

### Question Description

Given a function and one of its zeros find all of the zeros of the function:

2x^3 + 7x^2 - 53x - 28; x - 4

______________________________

Using the rational zero theorem, list all the possible rational zeros for the function:

p(x) = 6x^3 + 4x^2 - 14x + 4

## Final Answer

Since the highest exponential degreee of the equation is (3), then the equation has 3 zeros.

We already know one of the zeros: (x-4). Thus, we must divide the equation in order to get  new one. We will divide

(2x^3 + 7x^2 - 53x - 28) / (x-4)    using synthetic division

After divinding, we get a new equation:
2x^2 + 15x + 7
Now, we can use the quadratic formula to find the other 2 zeros.

We know that

a= 2

b= 15

c=7

We have found the three zeros:

1. (x - 4)
2. (x + 7)
3. (x + 1/2)

The Rational Zero Theorem.

You need to list all the possible factors of p (6) and q (4).

Also, all the values of (p/q). [Take into account that there are duplicates, just cross them out]

Now, you must use synthetic division with all values of (p/q) in order to determine if they are zeros. For example, I will use synthethic division with (1/3).

As you can see, there is no remainder. Therefore, 1/3 is one of the equation's zeros. You do the work for the other ones if you need it.

The three zeros for this equation are:

1. (x - 1/3)
2. (x - 1)
3. (x + 2)

Cesaraug (72)
Cornell University
Review

Anonymous
Top quality work from this tutor! I’ll be back!

Anonymous
Just what I needed… fantastic!

Anonymous
Use Studypool every time I am stuck with an assignment I need guidance.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors