Mathematics, 09.11.2020 16:50, NANA2007

Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicity: 3 Zero: 0, multiplicity: 2 Degree: 5

Answers: 2

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The polynomial for the conditions with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicity: 3 Zero: 0, multiplicity: 2 Degree: 5 is given as

$\rm\bold{ y(x) = 1\times (x-2)^3(x-0)^2 }$

According to the given condition

The given conditions to write the polynomial equations are as follows

Zero 2 and Multiplicity 3

Zero 0 and Multiplicity 2

Degree of polynomial expression = 5

Leading coefficient of polynomial expression = 1

Let us consider the polynomial equation has only one variable and hence in general form we can write the equation of polynomial as follows

$\rm y (x) = a(x-\alpha)^m (x-\beta)^n........(1)\\Where \\a = Leading \; coefficient\; of\; polynomial\; expression \\\alpha ,\beta = Roots \; of \; the\; polynomial\; expression\\m\; and \; n \; are \; multiplicities \; of \; the \; roots \; \alpha,\beta \; respectively\\Degree = m+n$

From the general form of polynomial expression as shown in equation (1) we can write

Polynomial expression for the given conditions is formulated in equation (2)

$\rm y(x) = 1\times (x-2)^3(x-0)^2 .......(2)$

So the polynomial for the conditions given in question is expressed as

$\rm\bold{ y(x) = 1\times (x-2)^3(x-0)^2 }$

For more information please refer to the link given below

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answered: amandasantiago2001

Given:

Zero: 2, multiplicity: 3

Zero: 0, multiplicity: 2

Degree: 5

Leading coefficient = 1

To find:

The polynomial function.

Solution:

The general form of a polynomial is

$P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}$

where, a is a constant, c_1,c_2,...,c_n are zeroes with multiplicity m_1,m_2,...,m_n .

Using the given information and the general form of a polynomial, we get

$P(x)=a(x-2)^{3}(x-0)^{2}$

P(x)=ax^2(x^3-6x^2+12x-8)

P(x)=a(x^5-6x^4+12x^3-8x^2)

Leading coefficient is 1, so the value of a is also 1.

P(x)=1(x^5-6x^4+12x^3-8x^2)

P(x)=x^5-6x^4+12x^3-8x^2

Therefore, the required polynomial is P(x)=x^5-6x^4+12x^3-8x^2 .

answered: Guest

Answer: choice c and choice d

=====================================

explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

Which functions have an additive rate of change of 3? check all that apply

answered: Guest

honestly bro aint no one got time to answer these dumb question just do it p***y

step-by-step explanation:

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Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and...