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
Alex17521 [72]
3 years ago
6

The polynomial of degree 3, P(x), has a root of. multiplicity 2 at x=1 and a roof of multiplicity 1 at x= -3. the y- intercept i

s y= 2.1. Find a formula for P(x)​
Mathematics
2 answers:
Stella [2.4K]3 years ago
6 0

P(x) has degree 3, so it takes the general form

P(x)=ax^3+bx^2+cx+d

It has a root x=1 of multiplicity 2, which means (x-1)^2 divides P(x) exactly, and it has a root of x=-3 of multiplicity 1 so that x+3 also is a factor. So

P(x)=a(x-1)^2(x+3)

Expanding this gives

P(x)=a(x^3+x^2-5x+3)=ax^3+ax^2-5ax+3a

\implies\begin{cases}a=b\\-5a=c\\3a=d\end{cases}

The y-intercept occurs for x=0, for which we have

P(0)=d=2.1

Then

3a=d\implies a=0.7

a=b\implies b=0.7

-5a=c\implies c=-0.14

So we have

\boxed{P(x)=0.7x^3+0.7x^2-0.14x+2.1}

Dafna11 [192]3 years ago
5 0

Answer:

4

Step-by-step explanation:

on edge.

You might be interested in
Help and explain explain !!!!!!!!!!
tigry1 [53]

Answer:

x=-1\text{ or }x=11

Step-by-step explanation:

For a=|b|, we have two cases:

\begin{cases}a=b,\\a=-b\end{cases}

Therefore, for 18=|15-3x|, we have the following cases:

\begin{cases}18=15-3x,\\18=-(15-3x)\end{cases}

Solving, we have:

\begin{cases}18=15-3x, -3x=3, x=\boxed{-1},\\18=-(15-3x), 18=-15+3x, 33=3x, x=\boxed{11}\end{cases}.

Therefore,

\implies \boxed{x=-1\text{ or }x=11}

3 0
3 years ago
Find the product of (3.7 × 104) and 2.
Debora [2.8K]

Answer:

A. The answer is 7.4x10^3

7 0
3 years ago
Use the graph below to write the equation of the function
Ksivusya [100]

Answer:

c

Step-by-step explanation:

gefhhfeyjhtwgi15287

8 0
3 years ago
A rectangle has an area of 40cm cubed and a length of eight cm sketch the rectangle and grind the width
crimeas [40]
40 divided by 8= 5
the width is 5
6 0
3 years ago
Need answers pls I am struggling!
Lady bird [3.3K]

Answer:

(1)....27

(2)...30

ans...............

6 0
3 years ago
Other questions:
  • What is a dependent clause???
    8·2 answers
  • Review
    14·1 answer
  • Wilma and Betty are playing a number game. Wilma tells Betty, "I'm thinking of a number between 1 and 10. If I take the number a
    9·1 answer
  • What is the scientific notation of 0.000000045?
    5·2 answers
  • I’m stuck. Need help on this one.
    11·1 answer
  • If [infinity]∑n=0cn9n is convergent, does it follow that the following series are convergent? (a) [infinity]∑n=0cn(−3)n
    7·1 answer
  • 40% of 320= 128 * 320=
    5·1 answer
  • 3, -2, -7,...<br> what is the common difference of this arithmetic sequence
    6·1 answer
  • Johnny wants to buy carpet to cover his whole living room, except for the tiled floor. The tiled floor is 7 1 2 ft by 3 1 4 ft.
    11·1 answer
  • What is the mean?<br> -9 -9 -3 -6 -7
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!