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
irinina [24]
3 years ago
11

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:
AfilCa [17]3 years ago
5 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
Complete the equations bellow.
Step2247 [10]
What equations? Explanation:
7 0
3 years ago
Explain how you would solve for the value of x when you are given the solution to a function.
Svetlanka [38]

Answer:

Substitute

Step-by-step explanation:

Substitute the values given in the function

and you will get the answer.

P.s. It depends on the question

3 0
3 years ago
There are 25 bananas that will be cut and divided evenly between 4 loaves of bread. How many bananas go into each loaf? Choose t
Paul [167]

Answer: 6 1/4

Step-by-step explanation: 25 divided by 4 = 6 1/4

4 0
3 years ago
What is the equation of the line that passes through the points (-1, 3) and (1, 11)
lina2011 [118]

Answer: To find the slope of this line, you would use the fomula

y2 - y1/ x2 - x1

11 - 3 / 1 - (-1)=

8/2

4

The slope of your line would be 4

3 0
3 years ago
Solve each system by substitution. please help me<br> 2x{+y=6<br> x{+y=3
saw5 [17]
1. x= 3/Y as a fraction btw

2. Same thing
6 0
3 years ago
Other questions:
  • SOMEONE PLEASE HELP ALL THE QUESTIONS R ATTACHED AS WELL AS THE ANSWERS!!!!!!!!!!!!!!
    13·1 answer
  • Which point represents -(-10) on the number line?
    5·1 answer
  • You are in charge of planning a barbecue. Hamburger costs $2 per pound and chicken costs $3 per pound. You have $30 to spend, th
    11·2 answers
  • Which of the following is the graph of y= start root -x -3 endroot?
    14·1 answer
  • 40 POINTS!!!!!!!!!!!!!!!!! Will mark Brainliest
    11·1 answer
  • A(-2,-2) B(-1,2) C(2,1) / A (-4,-4) (-2,4) C(4,2)
    11·1 answer
  • He makes a total of $500 for every 3 clients he
    6·2 answers
  • Simple Algebra problem. Includes the x and y axis. Also need help finding the perimeter.
    9·1 answer
  • Which number is the best approximation for π^2 : 9, 9.3, 9.6, or 9.9?​
    15·1 answer
  • Make an accurate drawing of two rectangles with the same perimeter, but different areas. Indicate the dimensions of the rectangl
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!