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Sophie [7]
3 years ago
15

How to write a polynomial function with rational coefficients in standard form with the given zeros?

Mathematics
1 answer:
Gennadij [26K]3 years ago
4 0
If you have as many zeros (z1, z2,... zn) as the degree of the polynomial function (n), then the function equation is given by:

f(x) = k (x - z1) (x - z2) ··· (x - zn)

where k is a constant. To determine this constant you need additional information (e.g. another point of the function).

You might also have less zeros than the degree of the polynomial, because some of them have a multiplicity greater than 1. Let z1,...,zr be the zeros, and m1,...mr be the multiplicity of each zero, where m1+m2+...+mr=n (we assume the sum of all multiplicities equals the degree of the polynomial). In this case, you can use:

f(x)=k(x-z_1)^{m_1} (x-z_2)^{m_2} \cdots (x-z_r)^{m_r}

Again, you have an undetermined constant factor.

From any of the two expressions above, you have to apply the distributive property to go on to the standard form.

An example: the zeros of a 3-degree polynomial function are -2, 1 and 3. The function equation is of this form:

f(x)=k(x+2)(x-1)(x-3) = k(x^3-2x^2-5x+6)

If you don't have all the zeros, or the sum of multiplicities does not equal the degree of  the polynomial, you have not enough information to write the equation of the function.

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Can someone please help??
Vsevolod [243]

Answer:

let the number of cows = x

let the number of chickens = y

since there are 42 heads:

x + y = 42

and since a cow has 4 legs, and a chicken has 2

4x + 2y = 144

from first equation:

x + y  = 42

x = 42 - y (now, we will substitute this in the second equation)

4(42 - y) + 2y = 144

168 - 4y + 2y  = 144

2y = 168 - 144

2y = 24

y = 12

now, we know the number of chickens. we will replace y with 12 in the first equation since it is more simpler

x + 12 = 42

x = 30

So, there are 30 cows and 12 chickens

Brainly it if you find the answer helpful

5 0
3 years ago
M is the midpoint of the segment. Find the length of XM.
Lelechka [254]

Answer:

x=2 and XM=11

Step-by-step explanation:

because M is the midpoint of the line, you know that both XM and ZM are equal and you know an expression for the lengths of both of these.

set these expressions equal and solve:

4x+3=3x+5 so by subtracting the 3x from the right side, moving it over to the left and subtracting 3 from the left side to move it over to the right, you get:

x=2

then to find XM, plug in this value of x to get XM=11

4(2)+3=11

4 0
2 years ago
A group of organs that work together together to perform a major function is called
Rasek [7]

Answer:

organ system

Step-by-step explanation:

Cells make up tissues, tissues make up organs, and organs make up organ systems.

8 0
3 years ago
Can someone please help?
castortr0y [4]
B- They are always congruent. Congruent means in agreement or harmony. But in this case, identical in form. Parallelograms are parallel on both sides, which makes them have congruent sides. 
P.S.- This is elementary level, no offense. 
5 0
3 years ago
$61.60 for parts and labor rate is $30.00 per hour total cost 136.60 how many hours will the job take? Write an equation and exp
cluponka [151]

Answer:

(136.60 - 61.60) / 30 = 2.5 hours

Step-by-step explanation:

First, subtract the cost of parts from the total: 136.60 - 61.60 = 75

Now you have the total labor cost. Divide by the hourly rate: 75 / 30 = 2.5

6 0
2 years ago
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