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
s2008m [1.1K]
3 years ago
12

The polynomial of degree 5, P(x) P(x) has leading coefficient 1, has roots of multiplicity 2 at x=5 and x=0, and a root of multi

plicity 1 at x=−1
Find a possible formula for P(x)
Mathematics
1 answer:
Savatey [412]3 years ago
7 0

Answer:

P(x) = x^5 -9x^4 + 10x^3 + 25x^2

Step-by-step explanation:

The given degree of the polynomial P(x)  = 5

The leading coefficient = 1

So, the general form of the polynomial  with degree 5 isx^5 + bx^4 + cx^3 + dx^2 + ex + f

Now root x =5 is of multiplicity 2, x = 0 of multiplicity 2, x = -1 of multiplicity 1

If x = a is the zero of the polynomial of multiplicity m, then ,(x-a)^m is the factor of the polynomial.

⇒(x-5)^2 is a factor of P(x)

(x-0)^2is another factor of P(x)

  (x +1) is the last factor of P(x)

So, P(x) = Product of all factors = (x-5)^2 (x)^2(x+1)

Solving the above expression , we get

P(x) = (x^2 + 25 -10x) (x^3 + x^2)  = x^3(x^2 + 25 -10x) +x^2(x^2 + 25 -10x) \\= x^5 + 25 x^3 -10x^4 + x^4 +25x^2 -10x^3 \\=x^5 -9x^4 + 10x^3 + 25x^2

Hence,  P(x) = x^5 -9x^4 + 10x^3 + 25x^2

You might be interested in
Amy can clean the interior of her car in 3 hours. If Amy and her husband work together,
leva [86]

Answer:

1 hour

Because 3 - 2  = 1.

Therefore, 1 hour only.

5 0
2 years ago
A 16-digit binary pattern converts to a ____ digit hexadecimal value.
Doss [256]

Solution -

In order to convert a binary number to hexadecimal ,we need to chunk the binary number into groups of 4 digits, adding 0 if necessary.

As the given number number is a 16 digit binary number, so when chunk in 4 digit groups, it will form 4 groups. Each group will represent a single digit in hexadecimal code.  

So, a 16-digit binary pattern converts to a 4 digit hexadecimal value.

7 0
3 years ago
Which number sentence has a difference of 5?<br> 8-(-3)<br> 0<br> -3-8<br> -3-(-8)<br> 3-(-8)
valina [46]

Answer:

The 4th one

Step-by-step explanation:

-3-(-8)=5

6 0
2 years ago
Mary is traveling cross country on a road trip. So far, Mary has traveled 200 miles in her car and 200 miles by train. The car t
VikaD [51]

Answer:

i dont know i think it is 11?!? srry if im wrong

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is the simplified expression for the expression below? 4(x + 8) + 5(x – 3)Which expression is equivalent to 6(x – 4)
Mashutka [201]

Answer:4x+32+5x-15

Step-by-step explanation: that’s the simplified equation, you would just have to distribute the 4 to its own equation and the 5 into its own equation.. but i think the second part of ur question is missing..

8 0
2 years ago
Other questions:
  • Estimate the value of 98.5x13
    14·2 answers
  • How do you do this?????????
    11·1 answer
  • How many fluid ounces equal 47 gallons
    5·2 answers
  • Suppose you cut a small square from a square of fabric as shown in the diagram. Write
    5·1 answer
  • 2 1/3 x 4 4/5as a fraction
    9·2 answers
  • Which of the following is a function and a relation?​
    9·1 answer
  • The function c(r)=2r+12.5 represents the cost c, in dollars, of riding r rides
    12·1 answer
  • Can you help me for this math? ​
    14·2 answers
  • 10.00 for movie tickets ​
    10·2 answers
  • Find the value of x for which line L is parallel to M
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!