List all of the possible rational zeros of each function

Asked by maham237 @ 31/12/2020 in Mathematics viewed by 278 People

List the possible rational zeros for each function.
1. f(x)= 2x^3 - 3x^2 + 4x - 18
2. f(x) = x^4 - 3x^2 + 2x + 24

Find the zeros of each function

3. f(x)= 2x^3 + 2x^2 - 8x -8
4. f(x)= x^3 + x^2 - 10x + 8

Answered by maham237 @ 31/12/2020

9514 1404 393

Answer:

{±1/2, ±1, ±3/2, ±2, ±3, ±9/2, ±6, ±9, ±18}
{±1, ±2, ±3, ±4, ±6, ±8, ±12 ±24}
-2, -1, 2
-4, 1, 2

Step-by-step explanation:

Possible rational zeros are of the form ...

±{divisor of the constant term}/{divisor of the leading coefficient}

1. Rational zeros will be one of ±{1, 2, 3, 6, 9, 18}/{1, 2}, so will be ...

{±1/2, ±1, ±3/2, ±2, ±3, ±9/2, ±6, ±9, ±18}

2. Rational zeros will be one of {±1, ±2, ±3, ±4, ±6, ±8, ±12 ±24}.

3. The pairs of coefficients suggest factoring by pairs:

f(x) = (2x^3 +2x^2) -(8x +8) = 2x^2(x +1) -8(x +1) = 2(x^2 -4)(x +1)

f(x) = 2(x -2)(x +2)(x +1)

Zeros of f(x) are 2, -2, -1, values of x that make the factors zero.

4. The sum of coefficients is zero, so x=1 is a zero. Factoring that out by any of several means, you find ...

f(x) = (x -1)(x^2 +2x -8)

The quadratic is factored by looking for factors of -8 that have a sum of 2. (4 and -2 are those)

f(x) = (x -1)(x +4)(x -2)

Zeros of f(x) are 1, -4, 2.

_____

The attached graph confirms our factoring of the polynomials of questions 3 and 4. For cubic and higher degree, I find a graphing calculator to be quite helpful finding zeros.

Use the rational root theorem to list all possible rational roots for the equation 3x^3+9x-6=0

Asked by maham237 @ 27/12/2020 in Mathematics viewed by 328 persons

Use the rational root theorem to list all possible rational roots for the equation. 3x^3+9x-6=0

What are the possible rational zeros of f(x) = x4 + 2x3 − 3x2 − 4x + 12?

Asked by maham237 @ 01/12/2020 in Mathematics viewed by 297 persons

How to determine the end behavior of a rational function

Asked by admin @ 11/11/2021 in Mathematics viewed by 246 persons

State the domain and end behavior of each rational function. Identify all horizontal and vertical asymptotes on the graph of each rational function. Then, verify your answer by graphing the …

How to find the end behavior of a rational function

Asked by admin @ 05/11/2021 in Mathematics viewed by 286 persons

State the domain and end behavior of each rational function. Identify all horizontal and vertical asymptotes on the graph of each rational function. Then, verify your answer by graphing the …

Which function returns a list of words in string

Asked by admin @ 17/08/2021 in Computer Science viewed by 293 persons

which of the following functions will return a list containing all words of the string. (a) find () (b) inder () (c) partition (d) split()

The work function of some metals is listed below

Asked by admin @ 11/08/2021 in Chemistry viewed by 268 persons

The work function (Ф) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is

List the functions of proteins in the text area below?

Asked by maham237 @ 14/07/2021 in Biology viewed by 327 persons

Which of the following is written as a rational function

Asked by maham237 @ 06/06/2021 in Mathematics viewed by 284 persons

A.G(x)=-2x B.P(x)=3x+4 C.Q(x)=x^2-8x+1 D.F(x)=x+2/5x

Is zero an irrational or rational number

Asked by maham237 @ 18/02/2021 in Mathematics viewed by 272 persons

If p and q are non-zero rational numbers, and s and t are irrational numbers, select all of the statements that are always false. The product pq is irrational. The …

List the functions of proteins in the text area below

Asked by maham237 @ 29/12/2020 in Biology viewed by 334 persons

List the functions of proteins in the text area below.

Asked by maham237 @ 02/12/2020 in Biology viewed by 367 persons

How to find x and y intercepts of rational functions

Asked by admin @ 27/11/2021 in Mathematics viewed by 328 persons

How do we find x-intercept of rational function

How to find the horizontal asymptote of a rational function

Asked by admin @ 25/11/2021 in Mathematics viewed by 278 persons

State the horizontal asymptote of the rational function. For full credit, explain the reasoning you used to find the horizontal asymptote. (5 points) f(x)= x^2+3x-2/x-2

How to find zeros of a function on a graph

Asked by admin @ 22/11/2021 in Mathematics viewed by 371 persons

What are the zeros of the function shown in the graph? −4, 0, 2 −2, 0, 4 −5, 0, 17 −17, 0, 5

Finding the x and y intercepts of a rational function

Asked by admin @ 22/11/2021 in Mathematics viewed by 342 persons

Task 3—Graphing Rational Functions Create a rational function with a linear binomial in both the numerator and denominator. -Part 1. Graph your function using technology. Include the horizontal and vertical …