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
goldenfox [79]
2 years ago
6

For the polynomial function ƒ(x) = x4 −25x2, find the zeros. Then determine the multiplicity at each zero and state whether the

graph displays the behavior of a touch or a cross at each intercept.

Mathematics
1 answer:
Veronika [31]2 years ago
7 0

<u>ANSWER</u>

The zeros are x=-5,x=0,x=5


EXPLANATION

Given;

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


We can rewrite the function as


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


\Rightarrow f(x)=x^2(x^2-5^2)


\Rightarrow f(x)=x^2(x-5)(x+5)



The zeros are found by equating the function to zero.


\Rightarrow x^2(x-5)(x+5)=0


\Rightarrow (x-5)=0

The multiplicity is 1, since it is odd the graph crosses at this intercept. which is x=5


Or

\Rightarrow (x+5)=0


The multiplicity is 1, since it is odd the graph crosses at this intercept. which is x=-5


Or


\Rightarrow x^2=0


This last root has a multiplicity of 2.

That is

x=0 repeats two times.


Since the multiplicity is even, the graph touches the x-axis at the point x=0.



See graph.









You might be interested in
Compare 6 ⋅ 108 to 3 ⋅ 106.
djverab [1.8K]

Answer:

6*10^8  is 200 times larger than  3*10^6

Step-by-step explanation:

6*10^8\ and \ 3*10^6

To compare both values we divide the exponents

\frac{6*10^8}{3*10^6}

6 divide by 3 is 2

for simplify exponents we use exponential property

a^m / a^n = a^(m-n)

\frac{10^8}{10^6}=10^2

\frac{6*10^8}{3*10^6}=2*10^2= 200

6*10^8  is 200 times larger than  3*10^6

4 0
3 years ago
Read 2 more answers
How to construct the circumcenter of a triangle?
Step2247 [10]
U just x it to the tingles
6 0
3 years ago
Read 2 more answers
The infinite geometric sum formula can be used to write 0.126126126...as a fraction. What is the numerator of this reduced fract
igor_vitrenko [27]

Answer:

B. 14 hope this helps

Step-by-step explanation:


6 0
2 years ago
Determine weather the following is real or complex <br> i^6-122-7i^2
Leona [35]

Answer:

Real

Step-by-step explanation:

i^6-122-7i^2

(i^2)^3-122-7i^2

(-1)^3-122-7×(-1)

-1-122+7

-123+7

-116

So the final answer is -116

7 0
3 years ago
What are the solutions of the equation x² = 49
olga55 [171]
To find x you do √49=x
5 0
2 years ago
Other questions:
  • Write down a division with an answer of 0.713
    14·1 answer
  • Marcus has 731 books. He puts about the same number of books on each of 9 shelves in his bookcase about how many books are on ea
    12·1 answer
  • Introduction to Functions
    14·1 answer
  • I need help solving this. Thanks in advance.
    9·1 answer
  • For #36, why is the answer 4? Plz explain.
    15·1 answer
  • 24.94 is 29% of what number? plz help
    6·1 answer
  • A runner incregses
    11·1 answer
  • Is this equation a direct variation? Y= 4x + 9
    8·1 answer
  • What is meaning of pictogram​
    8·1 answer
  • fertilizer you put 2 qts for every 50 gal of water I only want to use 15gal of water how many qts,pts,cups??? do i put
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!