Mathematics : asked on ozzy1146
 14.11.2022

The simplest polynomial function with zeros 7, square root 13 and 27i would be of what degree

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24.06.2023, solved by verified expert
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The simplest polynomial function is The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54.

Step-by-step explanation:

A n-th order polynomial in factorized form is defined by:

The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54(1)

Where:

The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54 - Independent variable.

The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54 - Dependent variable.

The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54, The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54,..., The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54, The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54 - Roots of the polynomial.

We know that three roots, two real and a complex root. By Quadratic Formula,  a second order polynomial has two conjugated complex number of the form The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54 and The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54. Hence, there is an additional zero: The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54.

By applying (1), we have the following polynomial when all roots are used:

The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54

By factorization and algebraic handling we have the simplest polynomial function:

The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54

The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54

The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54

The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54

The simplest polynomial function is The simplest polynomial function with zeros 7,, №17886169, 14.11.2022 23:54.

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Faq

Mathematics
Step-by-step answer
P Answered by PhD

The simplest polynomial function is y = x^{4}-(7+\sqrt{13})\cdot x^{3}+(27+7\sqrt{13})\cdot x^{2}-(189+27\sqrt{13})\cdot x + 189\sqrt{13}.

Step-by-step explanation:

A n-th order polynomial in factorized form is defined by:

y = (x-r_{1})\cdot (x-r_{2})\cdot ...\cdot (x-r_{n-1})\cdot (x-r_{n})(1)

Where:

x - Independent variable.

y - Dependent variable.

r_{1}, r_{2},..., r_{n-1}, r_{n} - Roots of the polynomial.

We know that three roots, two real and a complex root. By Quadratic Formula,  a second order polynomial has two conjugated complex number of the form a + i\,b and a - i\,b. Hence, there is an additional zero: -i\,27.

By applying (1), we have the following polynomial when all roots are used:

y = (x-7)\cdot (x-\sqrt{13})\cdot (x-i\,27)\cdot (x+i\,27)

By factorization and algebraic handling we have the simplest polynomial function:

y = [x^{2}-(7+\sqrt{13})\cdot x +7\sqrt{13}]\cdot (x^{2}+27)

y = x^{2}\cdot (x^{2}+27)-(7+\sqrt{13})\cdot [(x^{2}+27)]\cdot x+7\sqrt{13}\cdot (x^{2}+27)

y = x^{4}+27\cdot x^{2}-(7+\sqrt{13})\cdot x^{3}-(7+\sqrt{13})\cdot 27\cdot x +7\sqrt{13}\cdot x^{2}+189\sqrt{13}

y = x^{4}-(7+\sqrt{13})\cdot x^{3}+(27+7\sqrt{13})\cdot x^{2}-(189+27\sqrt{13})\cdot x + 189\sqrt{13}

The simplest polynomial function is y = x^{4}-(7+\sqrt{13})\cdot x^{3}+(27+7\sqrt{13})\cdot x^{2}-(189+27\sqrt{13})\cdot x + 189\sqrt{13}.

Mathematics
Step-by-step answer
P Answered by PhD

The solution is in the following image

The solution is in the following image
Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image 

Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

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