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alina1380 [7]
2 years ago
9

Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.

Mathematics
2 answers:
TiliK225 [7]2 years ago
7 0

we know that

For a polynomial, if x=a is a zero of the function, then (x−a) is a factor of the function. The term multiplicity, refers to the number of times that its associated factor appears in the polynomial.

So

In this problem

If the cubic polynomial function has zeroes at 2, 3, and 5

then

the factors are

(x-2)\\ (x-3)\\ (x-5)

Part a) Can any of the roots have multiplicity?

The answer is No

If a cubic polynomial function has three different zeroes

then

the multiplicity of each factor is one

For instance, the cubic polynomial function has the zeroes

x=2\\ x=3\\ x=5

each occurring once.

Part b) How can you find a function that has these roots?

To find the cubic polynomial function multiply the factors and equate to zero

so

(x-2)*(x-3)*(x-5)=0\\ (x^{2} -3x-2x+6)*(x-5)=0\\ (x^{2} -5x+6)*(x-5)=0\\ x^{3} -5x^{2} -5x^{2} +25x+6x-30=0\\ x^{3}-10x^{2} +31x-30=0

therefore

the answer Part b) is

the cubic polynomial function is equal to

x^{3}-10x^{2} +31x-30=0

Artemon [7]2 years ago
5 0
The quadratic function x^2 - 5x  + 6 =0
can be factored into (x -3) * (x-2)
And it would have roots of 3 and 2

So, if a cubic functions has roots of 2, 3 and 5 then its factors are
(x -2)* (x -3) * (x -5)
Multiply it out to get the equation.

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mamaluj [8]

Answer:

Given sequence is not a geometric progression and there will be no common ration for this sequence.

Step-by-step explanation:

Need to determine common ration for the following geometric sequence

32, 8, 2, 12, ...

In given geometric sequence  

a1 = 32, a2=8, a3=2, a4=12 ……….

Common ratio = \frac{a_2}{a_1} =\frac{a_3}{a_2} =\frac{a_4}{a_3}

\frac{a_2}{a_1}=\frac{8}{32}=\frac{1}{4}

\frac{a_3}{a_2} =\frac{2}{8}=\frac{1}{4}

\frac{a_4}{a_3}=\frac{12}{2}=6

Since \frac{a_2}{a_1}=\frac{a_3}{a_2}\neq\frac{a_4}{a_3}  so we can say that given sequence is not a geometric progression and there will no no common ration for this sequence.

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3 years ago
A Salesman worked on a weekly salary of $180.00 . To this was added a commission of 5% on all sales over $500. It his sales for
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company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26
podryga [215]

Answer:

t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435    

p_v =P(t_{(49)}  

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.

Step-by-step explanation:

Data given and notation  

\bar X=25.02 represent the sample mean

s=4.83 represent the sample standard deviation

n=50 sample size  

\mu_o =26 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is at least 26 mpg, the system of hypothesis would be:  

Null hypothesis:\mu \geq 26  

Alternative hypothesis:\mu < 26  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=50-1=49  

Since is a one sided test the p value would be:  

p_v =P(t_{(49)}  

Conclusion  

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.

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Answer:

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Step-by-step explanation:

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