What are the possible number of positive, negative, and complex zeros of f(x) = x6 – x5– x4 + 4x3 – 12x2 + 12 ?

Answers

Answer 1

Answer: This is a polynomial with more than 2 as a degree. Using Descartes Rule of Signs:
f(x) = x⁶ + x⁵ + x⁴ + 4x³ − 12x² + 12
Signs: + + + + − + 2 sign changes ----> 2 or 0 positive roots
f(−x) = (−x)⁶ + (−x)⁵ + (−x)⁴ + 4(−x)³ − 12(−x)² + 12 f(−x) = x⁶ − x⁵ + x⁴ − 4x³ − 12x² + 12
Signs: + − + − − + 4 sign changes ----> 4 or 2 or 0 negative roots
Complex roots = 0, 2, 4, or 6

Answer 2

Answer:

Descarte's Rule of Sign is useful for finding the zeroes of a polynomial. The rule will tell you how many roots you can expect and of which type not where the polynomial's zeroes are. This rule is given as follows:

$For \ a \ polynomial \ f(x)=a_(n)x^n+a_(n-1)x^(n-1)+ \ldots a_(2)x^2+a_(1)x+a_(0) \n \n with \ real \ coefficients \ and \ a_(0) \neq 0$

$\bullet \ The \ number \ of \ \mathbf{positive \ real \ zeros} \ of \ f \ is \ either \ equal \ to \n the \ number \ of \ variations \ in \ sign \ of \ f(x) \ or \ less \ than \ that \n number \ by \ an \ even \ integer. \n \n \bullet \ The \ number \ of \ \mathbf{negative \ real \ zeros} \ of \ f \ is \ either \ equal \ to \n the \ number \ of \ variations \ in \ signs \ of \ f(x) \ or \ less \ than \ that \n number \ by \ an \ even \ integer.$

That is, the function:

$f(x)=x^6-x^5-x^4+4x^3-12x^2+12 \n \n \n + \ - \ - \ + \ - \ + \n \n Has \ four \ changes \ in \ sign$

4, 2, or 0 positive roots

On the other hand, the function:

$f(-x)=(-x)^6-(-x)^5-(-x)^4+4(-x)^3-12(-x)^2+12 \n \n f(-x)=x^6+x^5-x^4-4x^3-12x^2+12 \n \n \n + \ + \ - \ - \ - \ + \n \n Has \ 2 \ changes \ in \ sign$

2, or 0 negative roots

Finally:

Complex roots: 0, 2, 4, or 6

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220kg to lb please it's homework

Answers

220 kg * 2.2046= 485.017 lb

What is the inverse function of d(x)= 2x-4

Answers

Formula for inverse function:
$d^(-1)(y)=?\ny=2x-4\n2x=y+4\nx= (y+4)/(2)\n d^(-1)(y)= (y+4)/(2)$

$y=2x-4 \n Replace \ x \ by \ y:\n x=2y-4\n Isolate \ y:\n 2y=x+4\n y=(x+4)/(2)\n \n \boxed{d^(-1)(x)=(x+4)/(2)}$

A circular cylinder has a radius between 5.50 and 6.00 cm and a volume of 225 cm3. Write an inequality that represents the range of possible heights the cylinder can have to meet this criterion to the nearest hundrenth of the centimeter.

Answers

Answer:

The answer is: 1.99<h<2.37

Step-by-step explanation:

The procedure is as followed

V=πr^2h

225=π(5.5)^2h

h=2.37

225=π(6)^2h

h=1.99

A parking garage charges $2 for the hour and $1 each additional hour. Fran has $9.90 to spend for parking. What is the greatest number of hours Fran can park

Answers

Answer:

Frank can park 8.9 hours at the highest

Step-by-step explanation:

Here, we want to know the greatest amount of time that Frank can park given the amount he has to spend on parking.

From the question, we are told that he pays $2 for the hour and an extra $1 per additional hour.

Now, let the number of additional hour he is going to park be x. The bill for the additional hours will be ; $1 * x = $x

By adding this to the initial $2, we have the total $9.90

So, mathematically;

2 + x = 9.90

x = 9.9 -2

x = 7.9 hours

Now, the initial hour he parked is 1 hour + number of incremental hours = 1 + 7.9 = 8.9 hours

On a Venn diagram, shade the region:
1. AnB
2. (BnC)nA

Answers

Answer:

hope it will be helpful to you

Step-by-step explanation:

anb shade and anbnc shade

Sharon’s turtle escaped from her backyard sometime in the last few hours. According to her calculations, the farthest the turtle could have gone is 4 blocks down the road in either direction. If Sharon lives on the 112th block of town, which equation can be used to find the block numbers that represent the farthest distance that the turtle may be?

Answers

The farthest distance of the turtle can be solved with the following equations:

x = 112 + 4
x = 112 - 4

By solving the equations, we conclude that the turtle can be found either in the 116th block or the 108th block.

Answer:

its B :)

Step-by-step explanation:

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