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
dusya [7]
3 years ago
9

Complete the steps to solve the polynomial equation x3 – 21x = –20. According to the rational root theorem, which number is a po

tential root of the polynomial?
Mathematics
1 answer:
jeka943 years ago
3 0

Answer:

Zeroes : 1, 4 and -5.

Potential roots: \pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20.

Step-by-step explanation:

The given equation is

x^3-21x=-20

It can be written as

x^3+0x^2-21x+20=0

Splitting the middle terms, we get

x^3-x^2+x^2-x-20x+20=0

x^2(x-1)+x(x-1)-20(x-1)=0

(x-1)(x^2+x-20)=0

Splitting the middle terms, we get

(x-1)(x^2+5x-4x-20)=0

(x-1)(x(x+5)-4(x+5))=0

(x-1)(x+5)(x-4)=0

Using zero product property, we get

x-1=0\Rightarrow x=1

x-4=0\Rightarrow x=4

x+5=0\Rightarrow x=-5

Therefore, the zeroes of the equation are 1, 4 and -5.

According to rational root theorem, the potential root of the polynomial are

x=\dfrac{\text{Factor of constant}}{\text{Factor of leading coefficient}}

Constant = 20

Factors of constant ±1, ±2, ±4, ±5, ±10, ±20.

Leading coefficient= 1

Factors of leading coefficient ±1.

Therefore, the potential root of the polynomial are \pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20.

You might be interested in
The length of a rectangular garden is 7 meters longer than its width. if its perimeter is ( 12 x + 14) meters, find its length i
cluponka [151]
L=7+w
P=(12x+14)=2(6x+7)
l+w= P/2 = 2(6x+7)/2= 6x+7
l+w=6x+7
2l = 6x+7
l = (6x+7)/2
l=7+w
-> w= l-7
= [(6x+7)/2] -7
= (6x+7-14)/2
= (6x-7)/2

7 0
3 years ago
What is the slope of the line?
vladimir1956 [14]

Answer:

8

Step-by-step explanation:

exponential growth

5 0
2 years ago
The price of a technology stock was $9.74 yesterday. Today, the price fell to $9.67. Find the percentage decrease. Round your an
agasfer [191]
% change = (new value - old value)/(old value) * 100%
.. = (9.67 -9.74)/9.74 * 100%
.. = -0.07/9.74 * 100%
.. = -0.7%

The decrease is 0.7%.
5 0
3 years ago
What are 3 different quotients that equal 4 to the negative 5th power
Ilia_Sergeevich [38]
4^-5=1/1024 or 2/2048 or 3/3072
8 0
3 years ago
A cone is formed from a 300-degree sector of a circle of radius 18 by aligning the two straight sides. what is the result when t
vampirchik [111]

The radius of the completed cone is

... 18×(300°/360°) = 15

The height of the completed cone is found from the Pythagorean theorem:

... 15² + h² = 18²

... h = √99 = 3√11

The volume is given by

... V = (1/3)πr²·h = (1/3)π·15²·3√11

Dividing this value by π gives 225√11 cubic units.

7 0
3 years ago
Other questions:
  • Tom wrote the number 45,378. Bill wrote the number 36,721.How many times greater is the 7 in bill number than the 7 in tom numbe
    13·1 answer
  • Circle o has circumference of 88pi cm. <br> what is the length of the radius of the circle ?
    6·2 answers
  • The distance from the library to the park is your point 7 km how many meters is this
    11·1 answer
  • Harold worked 27 hours at a rate of $13.25 per hour. Which line in the table will help him calculate his income tax for this wee
    6·1 answer
  • If 20 coins are tossed, find the probability that they'll all land on tails.
    9·1 answer
  • PLEASE HELP ME WITH THIS THX!!!!!<br>I REALLY NEED HELP WITH THIS!
    8·2 answers
  • Can you put 5(3+j+2j) as a verbal expression?
    13·1 answer
  • Assuming there’s is a proportional relationship which additional set of values could be included in the table
    14·2 answers
  • Half the sum of 8 and r​
    8·1 answer
  • Please answer with work shown (only if possible)
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!