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
EleoNora [17]
2 years ago
15

The function f(x) is a cubic function and the zeros of f(x) are -6, -3 and 1. The

Mathematics
1 answer:
jarptica [38.1K]2 years ago
3 0

Answer:

P(x)=-5x^3-40x^2-45x+90

Step-by-step explanation:

<u>Equation of a Polynomial</u>

Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written as:

P(x)=a(x-x1)(x-x2)(x-x3)

Where a is the leading coefficient.

We know the three roots of the polynomial -6, -3, and 1, thus:

P(x)=a(x+6)(x+3)(x-1)

Since the y-intercept of the polynomial is y=90 when x=0:

90=a(0+6)(0+3)(0-1)

90=a(6)(3)(-1)=-18a

Thus

a = 90/(-18) = -5

The polynomial is:

P(x)=-5(x+6)(x+3)(x-1)

We must write it in standard form, so we have to multiply all of the factors as follows:

P(x)=-5(x^2+6x+3x+18)(x-1)

P(x)=-5(x^2+9x+18)(x-1)

P(x)=-5(x^3-x^2+9x^2-9x+18x-18)

P(x)=-5(x^3+8x^2+9x-18)

\boxed{P(x)=-5x^3-40x^2-45x+90}

You might be interested in
I need help I’m on my last questionnn
LenKa [72]

Answer:

7.3 in

Step-by-step explanation:

Area of triangle = (1/2) *b*h

27 = (1/2) * x^2

54 = x^2

square root (54) = x

x=> 7.3484....

Rounding off to 1 decimal place, you get 7.3 in.

8 0
2 years ago
Read 2 more answers
What is a rational number between 9.6 and 9.7
lisov135 [29]
I'm pretty sure there are no rational numbers between 9.6 and 9.7
5 0
3 years ago
Read 2 more answers
Help ( correct answer ) 16÷(4)(2)-3(2)÷2+1
Bess [88]
16 ÷ (4)(2) - 3(2) <span>÷ 2+1
16 </span>÷ 8 - 6 <span>÷ 3
2 - 2
0

Answer: 0</span>
3 0
3 years ago
Read 2 more answers
The Cupcake Factory makes the pattern shown to the right using candy hearts on its Friday Special cupcake. Write an equation usi
ozzi
Nice...........have fun dude
7 0
2 years ago
1651.43 rounded to the nearest hundred
ikadub [295]

Answer:

1600

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Decrease 5 1/4 m by 50 cm. Answer has to be m.
    11·2 answers
  • PLEASEEEE HELP URGENT
    11·1 answer
  • Which set of points lies on the given graph? Number graph ranging from negative four to four on the x axis and negative four to
    12·2 answers
  • A rectangular shaped picture frame has a perimeter of 360 inches...The length of the picture frame is five times its width.Find
    15·2 answers
  • Rocco is trying to find the fraction that is equivalent to the decimal 0.012. His work is shown below. Step 1: 0.012 = StartFrac
    14·1 answer
  • WILL MARK BRAINLIEST
    15·2 answers
  • Kerry and three friends went out for dinner. They split a large pizza and each person had a salad and a soda. They want to leave
    11·1 answer
  • PLEASE HELP question is in the picture
    13·1 answer
  • Find the number. 1.5 of 20
    13·2 answers
  • Please help I’m on the middle of an exam<br><br> Use the diagram of ABCD to find x.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!