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
Stolb23 [73]
3 years ago
5

Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -2 (multiplicity 3), 3 (m

ultiplicity 1), and with f(0) = 120.​
Mathematics
2 answers:
Genrish500 [490]3 years ago
6 0

Answer:

Step-by-step explanation:

Polynomial f(x) has the following conditions: zeros of -2 (multiplicity 3), 3 (multiplicity 1), and with f(0) = 120.

The first part zeros of -2 means (x+2) and multiplicity 3 means (x+2)^3.

The second part zeros of 3 means (x-3) and multiplicity 1 means (x-3).

The third part f(0) = 120 means substituting x=0 into (x+2)^3*(x-3)*k =120

(0+2)^3*(0-3)*k = 120

-24k = 120

k = -5

Combining all three conditions, f(x)

= -5(x+2)^3*(x-3)

= -5(x^3 + 3*2*x^2 + 3*2*2*x + 2^3)(x-3)

= -5(x^4 + 6x^3 + 12x^2 + 8x - 3x^3 - 18x^2 - 36x - 24)

= -5(x^4 + 3x^3 - 6x^2 - 28x -24)

= -5x^4 - 15x^3 + 30x^2 + 140x + 120

oee [108]3 years ago
4 0

Answer:

Step-by-step explanation:

-2 is a root for 3 times and 3 is root for once

so (x+2)^3 * (x-3) is part of f(x)

the constant term there is 2^3*(-3)=-24

so there is a multiplier of 120/-24=-5

f(x) = 5 * (x+2)^3 * (x-3)

You might be interested in
Part 1.] Does the graph have even symmetry, odd symmetry, or neither?
QveST [7]
Part 1
The graph has even symmetry.  You can see that because it is symmetric with respect to the y-axis.
Functions that have even symmetry have the following property:
f(x)=f(-x)
Part 2
To answer this we can simply check if the property we mentioned earlier holds for this function.
sin(\frac{\pi}{2})\ne sin(-\frac{\pi}{2})
We can see that sine does not have even symmetry. 
In fact, sine function has the following property: 
sin(x)=-sin(x)
This is called odd symetry.
Part 3
Take a look at the function that you attached in the picture. We know that function has even symmetry. 
Reflection over x-axis and <span>180° rotation around the origin would give us -f(x). We would not end up with the same function, so these two are out. 
</span><span>90° rotation around the origin would mean we swapped x <span>and y</span> so that one is out too. R</span><span>eflection over the line y=x is a property of functions that have an odd symmetry.
We are left with reflection around y-axis and, as mentioned before, this is the property of evenly symmetric functions.</span>
4 0
3 years ago
If a cotton candy vendor has 16 blue cones which is 50% of the total number of cones, then how many TOTAL cones does he have i n
Tatiana [17]

Answer:

He has a total of 32 cones

Step-by-step explanation:

5 0
2 years ago
Name 3 non-collinear points
Evgen [1.6K]
Points A, B, C, D, E, F are called non - collinear points.
3 0
3 years ago
A rope 40m long is used to form a rectangle. If the length of the rectangle formed is 4m longer than the width. Calculate the ar
ivanzaharov [21]

Answer:

96 sq. m

Step-by-step explanation:

If the width is x, the length is x + 4 and since perimeter = 2 * (length + width), we can write:

40 = 2(x + x + 4)

40 = 2(2x + 4)

20 = 2x + 4

16 = 2x

x = 8 so x + 4 = 12, therefore the area is 8 * 12 = 96 square meters.

5 0
3 years ago
Read 2 more answers
700 is 35% of what number??
harina [27]

Answer:

245

Step-by-step explanation:

35                    x

-------             --------

100               700

then you cross multipy and you get

24500

------------------

100

cross out the zeros

and get 245

8 0
3 years ago
Other questions:
  • On Wednesday, Miguel's bank account balance was -$55. On Thursday, his balance was less than that. Use absolute value to describ
    5·1 answer
  • Are the polygons similar? If they are, write a similarity statement and give the scale factor.
    6·1 answer
  • How many people have been to Mexico, but not have been to Canada
    5·2 answers
  • I need help please.
    12·2 answers
  • An equilateral triangle has a perimeter of 18 feet. If a square whose sides have the same length as one side of the triangle is
    5·1 answer
  • The menu price of a sandwich at a restaurant is $6. The purchase is subject to a 5% food tax, and you would like to leave a tip
    6·2 answers
  • a bakery used 25% more butter this month than last month if the bakery used 240 kilograms of butter last month how much did it u
    7·1 answer
  • In the storage room, folders are stored in packages
    12·2 answers
  • (6 x 10^8) divide (1.5 x 10^-4)
    15·2 answers
  • Find the missing side lengths.<br><br> Can someone please help???
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!