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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)!!!

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Sergio [31]
What is your Question...
3 0
3 years ago
Two angles of a triangle measure 45 degrees and 90 degrees. What is the third angle measure?
neonofarm [45]

Answer:

B

Step-by-step explanation:

Angles in a triangle add up to 180

Take 45 + 90 then subtract the answer from 180

6 0
2 years ago
Sarah needs 30 liters of a 25% acid solution how many liters of the 10% and the 30% acid solutions should she mix to get what sh
sweet-ann [11.9K]

Answer:

7.5 L of 10% solution and 22.5 L of 30% solution

Step-by-step explanation:

Volume of 10% solution plus volume of 30% solution = total volume of 25% volume.

x + y = 30

Acid in 10% solution plus acid in 30% solution = total acid in 25% solution.

0.10 x + 0.30 y = 30 × 0.25

0.10 x + 0.30 y = 7.5

Solve the system of equations, using either substitution or elimination.  I'll use substitution:

x = 30 − y

0.10 (30 − y) + 0.30 y = 7.5

3 − 0.10 y + 0.30 y = 7.5

0.20 y = 4.5

y = 22.5

x = 30 − y

x = 7.5

Sarah needs 7.5 L of 10% solution and 22.5 L of 30% solution.

8 0
3 years ago
Read 2 more answers
Mixed Applications
Orlov [11]

The solution to the given question will be:-

A) If a number, n, divided by 8 equals 2.5, what is n: n = 20

B) The sum of a number, n, and 6.05 is 12.4. What is n: n = 6.35

C) Stacy is one-fourth as old as her mother. If Stacy's mother is

36, how old is Stacy: 9 years

<h3>What is an expression?</h3>

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division

A) If a number, n, divided by 8 equals 2.5, what is n?

n / 8 = 2.5

n = 8 x 2.5 = 20

B) The sum of a number, n, and 6.05 is 12.4. What is n?

n  + 6.05 = 12.4

n = 12.4 - 6.05 = 6.35

C)  Stacy is one-fourth as old as her mother. If Stacy's mother is

36, how old is Stacy?

(1 / 4) M_{age} = S_{age}

S_{age}  =  ( 36 / 4)

S_{age}  =  9 years

Therfore the answers are n = 20 ,n = 6.35, S_{age}  =  9 years

To know more about Expression follow

brainly.com/question/723406

#SPJ1

6 0
2 years ago
The sum of two numbers is 840. One of the numbers is 357. What is the other number?
Ksivusya [100]


We can create a formula first.

X will be the unknown number

840= 357+x
-357 -357

483 = x

Hope this helps
7 0
3 years ago
Read 2 more answers
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