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 .

Step-by-step explanation:

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

(1)

Where:

- Independent variable.

- Dependent variable.

, ,..., , - 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 and . Hence, there is an additional zero: .

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

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

The simplest polynomial function is .

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Mathematics

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

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:

- Independent variable.

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

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The last time Robert filled up his car with gas, he paid $24.50 for 7 gallons. This time, he needs 15 gallons. If the price is the same, how much will he pay?

Step-by-step answer

P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

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The answer is in the image

The answer is in the image

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P Answered by PhD

The total nom of code that can be used is equal to 5+3 = 8

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An online media service offers video and music downloads. Each download of a song costs $1. Each download of a video costs 5 times as much as the song download. You have a credit of $70. How many songs can you purchase after buying 12 videos?

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The answer is in the image

The answer is in the image

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The answer is in the image

The answer is in the image

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If a european swallow flies 15 meters every 1 second how many would kilometers would it fly in 15 minutes

Step-by-step answer

P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

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P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

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Picture frame built till now= 6/(3/4)

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The answer is in the image

The answer is in the image

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P Answered by PhD

30% of 420 are first year students

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=126 students

Student who are not in first year = 420-126

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