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2 years ago

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?

Mathematics

2 answers:

RideAnS [48]2 years ago

4 0

Three! -7/9, -1/4, and -4/3

garri49 [273]2 years ago

3 0

Answer with Step-by-step explanation:

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number can be considered a complex number with its imaginary part equal to zero.

Hence, the given polynomial equation has atleast 1 real root and atmost 3 real roots

(9x + 7)(4x + 1)(3x + 4) = 0

On solving this, we get

9x+7=0 or 4x+1=0 or 3x+4=0

i.e. x= -7/9 or x= -1/4 or x= -4/3

As we can see all the roots are real

Hence, number of real roots are:

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The heights of the trees for sale at two nurseries are shown below. Heights of trees at Yard Works in feet : 7, 9, 7, 12, 5 Heig

Troyanec [42]

Answer:

The mean of tree heights at Yard Works is 8 feet and at Grow Station is 9 feet.The mean absolute deviation of the tree heights at both yards is 2.

Step-by-step explanation:

1). Height of the trees at Yard Works are = 7,9,7,12,5 feet

So mean height of the trees = (7+9+7+12+5)÷5

= 40÷5 =8 feet

Standard deviation of the trees at Yard works = ∑(║(height of the tree-mean height of the tree))║/(number of trees)

(height of the tree-mean height of the tree)= ║(7-8)║+║(9-8)║+║(7-8)║+║(12-8)║+║(5-8)║ = (1)+1+(1)+4+(3)= 10

Therefore standard deviation = (10)/(5) =2

2). In the same way mean height of the trees at Grow Station=(9+11+6+12+7)/5= 45/5 = 9

Now we will calculate the mean deviation of the tress at Grow Station

= ∑║(height of the tree-mean height of the tree)║/(number of trees)

= ║(9-9)║+║(11-9)║+║(6-9)║+║(12-9)║+║(7-9)║/(5)

= (0+2+3+3+2)/5

= 10/5 =2

Therefore The mean of tree heights at Yard Works is 8 feet and at Grow Station is 9 feet.The mean absolute deviation of the tree heights at both yards is 2.

7 0

2 years ago

Read 2 more answers

What is the solution set of the quadratic inequality 6x^2+1 greater than or equal to 0?

Ratling [72]

Answer:

Step-by-step explanation:

6x^2 + 1 <= 0

6x^2 <= -1

x^2 <= -1/6

Since we cannot take the square root of a negative number, there is no solution.

7 0

2 years ago

Write the coordinates of the vertices after a rotation of 180 degrees counterclockwise around the origin.

Umnica [9.8K]

90 degrees you are looking to your side

180 degrees you are looking behind you

around origin of 0,0

the image is flipped into the negative world if it is in posiitve or vice versa

8 0

2 years ago

What is the approximate length of arc s on the circle below? Use 3.14 for Pi. Round your answer to the nearest tenth.

slega [8]

Answer:

The approximate length of arc s is 14.1 inches

Step-by-step explanation:

<u><em>The picture of the question in the attached figure</em></u>

step 1

Find the circumference of the circle

The formula to calculate the circumference is equal to

$C=2\pi r$

we have

$r=6\ in\\\pi=3.14$

substitute

$C=2(3.14)(6)\\C=37.68\ in$

step 2

Find the approximate length of arc s

we know that

The circumference of a circle subtends a central angle of 360 degrees

using proportion

Find the arc length s for a central angle of 135 degrees

$\frac{37.68}{360}=\frac{x}{135}\\\\x=37.68(135)/360\\\\x= 14.1\ in$

4 0

2 years ago

Read 2 more answers

The fuel efficiency for a 2007 passenger car was 31.2 mi/gal. For the same model of car, the fuel efficiency increased to 35.6 m

Ierofanga [76]

We have been given that fuel efficiency for a 2007 passenger car was 31.2 mi/gal and the same model of car, the fuel efficiency increased to 35.6 mi/gal in 2012. Also, the gas tank for this car holds 16 gallons of gas.

We need to write a function and graph a linear function that models the distance that each car can travel for a given amount of gas up to one tankful.

Let represent the functions as $d_{1}(x)$ and $d_{2}(x)$ where $d_{1}$ and $d_{2}$ represent the distances traveled by car in years 2007 and 2012 and x represents the number of gallons. Therefore, we can express the required functions as: