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
spin [16.1K]
3 years ago
5

Which polynomial function has x intercepts -1,0, and 2 and passes through the point (1,-6)?

Mathematics
1 answer:
nikitadnepr [17]3 years ago
5 0

Answer:

f(x) = 3x^3 - 3x^2 - 6x

Step-by-step explanation:

Which polynomial function has x intercepts -1,0, and 2 and passes through the point (1,-6)?

There are 3 distinct and real roots given in the question, which means that the  function must be a third degree polynomial. The roots are -1, 0, and 2. This means that f(x) = 0 at these points. The general form of the cubic equation is given by:

f(x) = ax^3 + bx^2 + cx + d; where a, b, c, and d are arbitrary constants.

From the given data:

f(-1)=0 implies a*(-1)^3 + b*(-1)^2 + c(-1) + d = -a + b - c + d = 0. (Equation 1).

f(0)=0 implies a*(0)^3 + b*(0)^2 + c(0) + d = 0a + 0b + 0c + d = 0. (Equation 2).

f(2)=0 implies a*(2)^3 + b*(2)^2 + c(2) + d = 8a + 4b + 2c + d = 0. (Equation 3).

f(1)=0 implies a*(1)^3 + b*(1)^2 + c(1) + d = a + b + c + d = -6. (Equation 4).

Equation 2 shows that d = 0. So rest of the equations become:

-a + b - c = 0;

8a + 4b + 2c = 0;  (Divide 2 on both sides of the equation to simplify).

a + b + c = -6

This system of equation can be solved using the Gaussian Elimination Method. Converting the system into the augmented matrix form:

• 1 1 1 | -6  

• -1 1 -1 | 0

• 4 2 1 | 0

Adding row 1 into row 3:

• 1 1 1 | -6  

• 0 2 0 | -6

• 4 2 1 | 0

Dividing row 2 with 2 and multiplying row 1 with -4 and add it into row 3:

• 1 1        1 | -6

• 0 1       0 | -3

• 0 -2 -3 | 24

Multiplying row 2 with 2 and add it into row 3:

• 1 1       1 | -6

• 0 1       0 | -3

• 0 0 -3 | 18

It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• a + b + c = -6

• b  = -3

• -3c = 18 (This implies that c = -6.)

Put c = -6 and b = -3 in equation 1:

• a + (-3) + (-6) = -6

• a = -6 + 3 + 6

• a = 3.

So f(x) = 3x^3 - 3x^2 - 6x (All conditions are being satisfied)!!!

You might be interested in
Please answer <br>✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️​
Levart [38]

Step-by-step explanation:

Any known 0 number with exponent 0 is known as undefined

If 2^x = 16, then the value of x is 4

Writing separated multiplication of numbers in short form is called product of powers property

If base is negative and exponent is odd the expression has negative value

True/false:

True

False

True

True

5 0
3 years ago
1. Alex bought 2 buckets of baseballs that cost $19.49 each, a bat that cost $125.50, and 2 pair of baseball socks that totaled
Blizzard [7]

Answer:

$90.02

Step-by-step explanation:

<u>Solve</u>

Formula: Change money = paid money – bill. Paid money = change + bill.

Given: <em>2</em> buckets of baseballs that cost $<em>19.49</em> each

A bat that cost $<em>125.50</em>, and <em>2</em> pairs of baseball socks that totaled $<em>29.50</em>

Tax on Alex's purchases equaled $<em>16</em>.

Paid with three $<em>100</em> bills.

To find: How much change Alex received if he paid with three $100 bills

Total payment + Total Tax  -Total cost

19.49 + 125.50 + 29.50  = 174.49 (Don't add the $16 tax because that will be taken from the amount we pay)

∴, <em>three </em>100 bills is 300

So, 300 - 174.49 = 109.51

109.51 - 16 = 90.51

90.51 - 0.49 = $90.02

8 0
3 years ago
Max charges $3.50 per hour when he mows lawns, plus $6.00 for transportation expenses. Which function rule represents the amount
givi [52]
Max charges 12.30 cents
3 0
3 years ago
What is144 dividend by 10?
jeka94
14.4 is going to be your answer
7 0
3 years ago
Read 2 more answers
What is the possible value of x in the equality x&lt;3
algol13

Any value that is less than 3 but not equal to 3

4 0
3 years ago
Other questions:
  • A
    7·1 answer
  • In fraction form, what is 3/5÷1/3?<br><br>Thank you if answered
    12·2 answers
  • Write the expression 12(-2) in simplest form
    5·1 answer
  • Pam buys the following item a a shirt
    5·1 answer
  • Evaluate the expression solve for s = -1
    15·2 answers
  • Rectangle PQRS is rotated 90 counterclockwise about the origin what are the coordinates of point Q
    15·2 answers
  • Imagine each letter of the word mathematical is written on idividual pieces of paper and placed in a bag. should you pick a rand
    13·1 answer
  • Can you help me solve this?​
    8·1 answer
  • PLEASE HELP ASAP, MARKING BRAINLIEST!!!
    5·1 answer
  • A company made a storage container with sheet steel walls. The container was in the shape of a rectangular prism, as shown below
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!