1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alina [70]
3 years ago
15

Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?

Mathematics
2 answers:
igomit [66]3 years ago
8 0

Answer:

Option 1 is correct.

Step-by-step explanation:

The given polynomial is

f(x)=20x^4+x^3+8x^2+x-12

we have to find  all the rational roots of the polynomial f(x)

The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number i.e in the form of \frac{p}{q}

where p is a factor of constant term and q is the factor of coefficient of leading term.

In the given polynomial the constant is -12 and the leading coefficient is 20.

\text{All possible factor of -12 are }\pm1,\pm2, \pm3, \pm4,\pm6,\pm12

\text{All possible factor of 20 are }\pm1,\pm2,\pm4,\pm5,\pm10,\pm20

So, the all possible rational roots of the given polynomial are,

\pm1,\pm2, \pm3, \pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5},\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}

Now, the rational roots of polynomial satisfy the given polynomial

f(-\frac{4}{5})=20(-\frac{4}{5})^4+(-\frac{4}{5})^3+8(-\frac{4}{5})^2-\frac{4}{5}-12=\frac{256}{625}\times 20-\frac{64}{125}+\frac{128}{125}-\frac{4}{5}-12

=\frac{1024}{125}-\frac{64}{125}+\frac{128}{25}-\frac{4}{5}-12

=\frac{960}{125}+\frac{128}{25}-\frac{4}{5}-12=12-12=0

Hence, rational root.

f(\frac{3}{4})=20(\frac{3}{4})^4+(\frac{3}{4})^3+8(\frac{3}{4})^2+\frac{3}{4}-12=\frac{405}{64}+\frac{27}{64}+\frac{9}{2}+\frac{3}{4}-12=0

rational root

f(1)=20(1)^4+(1)^3+8(1)^2+1-12=20+1+8-11=18\neq 0

not a rational root.

hence, option 1 is correct

masya89 [10]3 years ago
7 0

Answer:

A. "-4/5 and 3/4"

Step-by-step explanation:

You might be interested in
Please help me!!! I have more points for this!
olga2289 [7]

Answer:

Thanks for the points :)>

Step-by-step explanation: yeahhh shawtyyy

7 0
3 years ago
What is the cubed root of 27?
lianna [129]

Answer:

Then answer is 3

Step-by-step explanation:

cube root = ³√27

3×3×3 = 3³ = 27

6 0
3 years ago
Read 2 more answers
If the value of 2x3 is 2, then what is the value of x?
Oduvanchick [21]
ANSWER: x = 1/3

WORKING OUT:

2 times x times 3 = 2

6 times x = 2

x = 1/3
5 0
3 years ago
George invested $18,500 five years ago and unfortunately the investment has been losing 6% of its value each year. What is the c
Naddika [18.5K]

Answer:

noice

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Solve for x please<br> 4.5x + 11.5 = 8.5x + 3.5
leonid [27]

Answer: have you tried to use photomath?


6 0
3 years ago
Read 2 more answers
Other questions:
  • Please assist on two questions, is offering 30+ points!
    7·1 answer
  • Write each of the following expressions without using the absolute value sign. |x−4| if x&gt;4
    10·1 answer
  • Divide the following polynomials. Write the answer in descending powers of a.
    14·2 answers
  • AVENGERS: The Avender movie made $1.6 million in ticket sales. Its sequel made $0.8 million in ticket sales. How much more than
    8·1 answer
  • During the school year, each student planted 2 x 10^2 trees as part of a community service project. If there are 3.5 x 10^3 stud
    8·1 answer
  • 2cm<br> 10<br> 2.5 cm<br> 2.5 cm<br> 2 cm<br> 3 cm<br> 6 cm<br> 5 cm
    5·1 answer
  • In an exponential function f(x)=a(b)^x it is known that f(5)=15 and f(7)=170. Which of the following is the closest to the value
    7·1 answer
  • I need help!!!!!!!!!!! Plz
    9·1 answer
  • What is the value of x for 10x+1=3(4x+2)-3? ​
    14·1 answer
  • What digit 7 sits in this number 714,583​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!