Mathematics, 20.09.2019 01:30 Greekfreak

Which polynomial function f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity 1, and root –5 with multiplicity 3?
f(x) = 3(x + 5)(x + 4)(x – 2)(x – 9)
f(x) = 3(x – 5)(x – 4)(x + 2)(x + 9)
f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x – 2)(x – 9)
f(x) = (x – 5)(x – 5)(x – 5)(x – 4)(x + 2)(x + 9)

Answers: 2

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Answers

The required polynomial function is $\bf f\left(x\right) =\left( {x+5}\right)\left({x+5}\right)\left({x+5}\right)\left({x+4}\right)\left({x - 2}\right)\left( {x-9}\right)$ .

Further explanation:

From the given problem, it is observed that for the required function f(x) there are 6 roots which are -4,2,9,-5,-5 and . It is possible only for the functions $f\left(x\right)=\left({x+5}\right)\left( {x+5}\right)\left({x+5}\right)\left( {x+4}\right)\left( {x -2}\right)\left({x -9}\right)$ or $f\left(x\right)=\left({x-5}\right)\left( {x-5}\right)\left({x-5}\right)\left({x-4}\right)\left({x + 2}\right)\left( {x+9}\right)$ .

Since, the coefficients of all for both the function is 1, the leading coefficient of both the function is 1.

The roots of the polynomial function $f\left(x\right)=\left({x+5}\right)\left({x+5}\right)\left({x+5}\right)\left({x+4}\right)\left({x -2} \right)\left({x-9}\right)$ is obtained as follows:

$\left({x+5}\right)\left({x+5}\right)\left({x+5}\right)\left({x+4}\right)\left({x-2} \right)\left( {x -9}\right) = 0$

Solution 1:

$\begin{aligned}\left( {x+5}\right)\left({x+5}\right)\left({x+5}\right)&= 0\hfill\\ x &=-5\,\,\,\,\,\,\,\,\,\,\left( {{\text{with multiplicity 3}}}\right)\hfill\\\end{aligned}$

Solution 2:

$\begin{aligned}\left({x+4}\right)&=0\hfill\\x&=-4\,\,\,\,\,\,\,\,\,\,\left( {{\text{with multiplicity 1}}} \right)\hfill\\ \end{gathered}$

Solution 3:

$\begin{aligned}\left( {x-2} \right)&=0\hfill \\ x&=2\,\,\,\,\,\,\,\,\,\,\left( {{\text{with multiplicity 1}}}\right)\hfill\\ \end{aligned}$

Solution 4:

$\begin{aligned}\left({x - 9} \right)&=0\hfill\\x&=9\,\,\,\,\,\,\,\,\,\,\left( {{\text{with multiplicity 1}}}\right)\hfill\\ \end{aligned}$

Therefore, the zeros of the polynomial function $f\left(x\right)=\left({x+5}\right)\left({x+5}\right)\left({x+5}\right)\left({x+4}\right)\left( {x -2}\right)\left({x-9}\right)$ are -4,2,9,-5,-5 and .

Thus, the required polynomial function is $\bf f\left(x\right) =\left( {x+5}\right)\left({x+5}\right)\left({x+5}\right)\left({x+4}\right)\left({x - 2}\right)\left( {x-9}\right)$ .

Learn more:

1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12

3. what are the domain and range of the function f(x) = 3x + 5?

Answer Details :

Grade: High School.

Subject: Mathematics.

Chapter: linear equation.

Keywords:

Polynomial function, root, zeroes, solution, multiplicity, f(x)=(x+5)(x+5), linear equation, quadratic, cubic expression, linear equation, zeros, function, substitution, origin, shaded, region, solution of inequality graph.

Answer from: Quest

answer: i believe it’s 245.04

step-by-step explanation:

Answer from: Quest

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

A. name the streets that are parallel to golden gate. b. name the streets that intersect 6th street.

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Which polynomial function f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity...