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
What is the retail price of the original price $60 markup : 15%
Nataly [62]
I think the original price is either $51 or $69
4 0
3 years ago
Read 2 more answers
Solve x2 - 10x = -21
ipn [44]

Answer:

add 21 to both sides to get everything on one side

x^2 - 10x + 21 = 0

do factorization, guess and check

(x - 7) (x -3) = 0

x =7, and x =3

8 0
3 years ago
Read 2 more answers
there are 15 black marbles and 10 white marbles in a bag. If you pick a marble from the bag without looking, what are your chanc
satela [25.4K]

Answer: 40%

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
At a zoo, 3 pandas eat a total of 181 1 2pounds of bamboo shoots each day. The male panda eats 3 times as much as the baby. The
S_A_V [24]

Answer:

6037.2 pounds of bamboo shoots does the female panda eat.

Step-by-step explanation:

Total pandas = 3

Total bamboo shoots eaten = 18112 pounds

Let baby panda eats bamboo = x

Male panda eats bamboo= 3x

Female panda eats bamboo = 2x

So, the equation will become

x+3x+2x=18112

Now solving the equation to find value of x

x+3x+2x=18112\\6x=18112\\x=\frac{18112}{6}\\x=3018.6

The value of x we get : x=3018.6

So, baby panda eats bamboo shoots = 3018.6 pounds

Male panda eats bamboo shoots = 3x = 3(3018.6) = 9055.8 pounds

Female panda eats bamboo shoots = 2x = 2(3018.6)= 6037.2 pounds

So, 6037.2 pounds of bamboo shoots does the female panda eat.

6 0
3 years ago
Which graph represents a linear function? (4 points)
leonid [27]

Answer:

On the surface, it seems easy. Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42?

That turned out to be much harder—as in, no one was able to solve for those integers for 65 years until a supercomputer finally came up with the solution to 42. (For the record: x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631. Obviously.)

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • Tell whether (-2,3)is a solution of 2y+x=4?
    8·2 answers
  • Rewrite 3.47 • 10^5 in standard form
    5·1 answer
  • T.L Hanna High School’s theatre department is putting on their annual play. Tickets (t) are $12 each. Parking is $5 flat. You an
    11·1 answer
  • A hot air balloon descended 99.6 meters in 12 seconds. What was the balloon's average rate of descent in meters per second?
    9·2 answers
  • A box contains six white balls, eight black balls, and five red balls. How many red balls must be added to the box to the probab
    14·1 answer
  • During the past half hour, a restaurant has had 23 orders for Pepsi and 15 orders for Mountain Dew. How many more orders have th
    13·1 answer
  • Don't understand how to do it<br>f(n)= 23+8(n-1)<br>​
    13·2 answers
  • 1. A normal male adult's pulse beats 360 times in
    9·1 answer
  • Give proof and show work and ill give brainliest
    5·1 answer
  • The histogram shows the prices of dinners at a local fine-dining restaurant.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!