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
Tamiku [17]
3 years ago
7

What are all of the real roots of the following polynomial? f(x) x^4-24x^2-25

Mathematics
2 answers:
Delicious77 [7]3 years ago
4 0

Answer:

The real roots are  ±5

Step-by-step explanation:

It is given that,

f(x) = x^4 - 24x^2 - 25

<u>To find the real roots</u>

Let x^4 - 24x^2 - 25 = 0 ----(1)

Take y = x^2

Then eq (1) becomes,

y^2 - 24y - 25 = 0

By using splitting method we can write,

y^2 + y - 25y - 25 = 0

y(y + 1) - 25(y +1) = 0

(y + 1)(y - 25) = 0

(x^2 + 1 )(x^2 - 25) = 0

From (x^2 + 1 ) we get complex roots

x^2 = -1

x = √-1

x - 25 = 0 we get real roots

x = 25

x = ±5

Therefore the real roots are  ±5

Greeley [361]3 years ago
3 0

<u>Answer:</u>

x = ±5

<u>Step-by-step explanation:</u>

We are given the following polynomial function and we are to find all of its real roots:

x^4-24x^2-25

Let y=x^2 so we can now write it as:

y^2-24y-25

Factorizing it to get:

(y^2+y)+(-25y-25)

y\left(y+1\right)-25\left(y+1\right)

\left ( y + 1 \right ) \left ( y - 2 5 \right)

Substitute back y=x^2 to get:

\left ( x^2 + 1 \right ) \left ( x^2 - 25 \right )

\left ( x^2 + 1 \right ) \left ( x + 5 \right ) \left ( x - 5 \right )

The quadratic factor has only complex roots. Therefore, the real roots are x = ±5.

You might be interested in
8) A total of 1456 people attended a high school football game. The cost was $5 for adults and $2.50 for students. If the
MAXImum [283]

Answer:

the answer is 762 adults and 694 students.

Step-by-step explanation:

762 x 5.00 = 3810

694 x 2.50 = 1735

now add 3810 + 1735 = 5545

8 0
3 years ago
Solve for f is h=2f/m+1
Natasha_Volkova [10]
H=2f/m+1
subtract one from both sides
h-1=2f/m
multiply m to both sides
m*h-1=2f
divide 2 both sides
mh-1/2=F
<span>(the whole left side of the equation is divided by 2 i just cant do it on the computer)</span>
7 0
3 years ago
Complete factorization f(x)=x^4-x^3-5x^2-x-6
Marianna [84]

The solution to the above  factorization problem is given as f′(x)=4x³−3x²−10x−1. See steps below.

<h3>What are the steps to the above answer?</h3>

Step 1 - Take the derivative of both sides

f′(x)=d/dx​​(x^4−x^3−5x^2−x−6)

Step 2 - Use differentiation rule d/dx​(f(x)±g(x))=d/dx​(f(x))±d/dx​(g(x))

f′(x)=d/dx​​(x4)−d/dx​​(x^3)−d/dx​​(5x^2)−d/dx​​(x)−d/dx​​(6)

f′(x)=4x^3−d/dx​​(x3)−d/dx​​(5x^2)−d/dx​​(x)−d/dx​​(6)

f′(x)=4x^3−3x2−d/dx​​(5x^2)−d/dx​​(x)−d/dx​​(6)

f′(x)=4x^3−3x^2−10x−d/dx​​(x)−d/dx​​(6)

f′(x)=4x^3−3x^2−10x−1−dxd​(6)

f′(x)=4x^3−3x^2−10x−1−0

Learn more about factorization:
brainly.com/question/25829061
#SPJ1

5 0
2 years ago
Solve this question please
WITCHER [35]

Answer: Its hard to explain, so I'll just give you the answer (47 degrees)

7 0
3 years ago
Read 2 more answers
The measure of an angle is 84.9°. What is the measure of its complementary angle?
joja [24]
The answer will most likely be 56 degrees try that it should be the answer!
8 0
3 years ago
Other questions:
  • HELP!! Simplify the expression 3y^2 • 4x^2y • 5x Using the laws of exponents. Show each step of your work.
    8·1 answer
  • A fundraiser lottery draws two winners each month from 50 tickets numbered
    8·1 answer
  • The Storm roller coaster climbs to a height of 180 feet. The Snake roller coaster climbs to a height of 105 feet. How much highe
    14·2 answers
  • One reading at an article research station showed that the temperature was -35 ��
    10·1 answer
  • Flip a coin 100 times. We want the chance of getting exactly 50 heads. What is the exact probability, correct to six decimal pla
    10·1 answer
  • Debbie buys a tree for the holidays. She would like to determine the amount of space it will take up in her living room. The tre
    14·1 answer
  • A lawn service owner is testing new weed killers. He discovers that a particular weed killer is effective 89% of the time. Suppo
    7·2 answers
  • What is the digit to the right of the decimal point in the decimal form of 4/37<br> ?
    6·1 answer
  • Determine whether the value is a discrete random​ variable, continuous random​ variable, or not a random variable. a. The number
    13·1 answer
  • The diameter of each circular hole in a paint palette is 42 millimeters.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!