How do I use the Descartes Rule of Signs to determine all possible number of positive and negative zeros?

f(x)= x^4-2x^3-4x^2+2x+3​

Answers

Answer 1

Answer:

We conclude that:

2  or 0 positive real roots2  or 0 negative real roots

Step-by-step explanation:

Descartes Rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is:

Either equal to the number of sign differences between consecutive nonzero coefficients, Or is less than it by an even number.

Given the function

[tex]f\left(x\right)=x^4-2x^3-4x^2+2x+3[/tex]

So, the coefficients are 1, −2, −4, 2, 3

As can be seen, there are 2 changes.

This means that there are 2 or 0 positive real roots.

To find the number of negative real roots, substitute x with -x in the given polynomial:

[tex]x^4-2x^3-4x^2+2x+3[/tex]  becomes [tex]x^4+2x^3-4x^2-2x+3[/tex]

The coefficients are 1, 2, −4, −2, 3

As can be seen, there are 2 changes.

This means that there are 2 or 0 negative real roots.

Therefore, we conclude that:

2  or 0 positive real roots2  or 0 negative real roots


Related Questions

Joe collects Pokemon cards. He already has 100 and buys a dozen more each week when he goes to the store. Jessica also collects Pokemon cards. She has 130 cards, and buys 6 more each week at the store.After how many weeks would the two kids have the same amount of cards?​

Answers

Answer:

5 weeks

Step-by-step explanation:

To find the answer to this question we have to write an equation for both situation and put them equal to each other.

Let's write an equation for Joe:

12x + 100

Now, for Jessica

6x + 130

Next, put them equal to each other:

12x + 100 = 6x + 130

Solve:

12x + 100 = 6x + 130

6x + 100 = 130

6x = 30

x = 5

Therefore, it will take 5 weeks for Joe and Jessica to have the same amount of cards.

Check:

12(5) + 100 = 6(5) + 130

60 + 100 = 30 + 130

160 = 160

I hope this helps!!

- Kay :)

Together, teammates Pedro and Ricky got 2678 base hits last season. Pedro had 282 more hits than Ricky. How many hits did each player​ have?

Answers

Answer:

pedro- 1621

ricky- 1057

Step-by-step explanation:

how do you write 2x simplified?

Answers

Answer:

Simplify the numerator with the sine expression by taking A = B = x and simplify the denominator using A = x and B = 2x. The resulting denominator will have sin (2x) and cos (2x) which you can write in terms of sin (x) and cos (x) using the expressions above.

Step-by-step explanation:

3х + y 2 – 7
Linear inquality

Answers

Answer:

xfgn  

Step-by-step explanation:

A triangular plot of land has sides of lengths 420 feet, 330 feet, and 180 feet. Approximate the smallest angle between the sides. The choices are rounded to the nearest degree.
A. 30 degree
B. 27 degree
C. 22 degree
D. 24 degree

Answers

Answer:

D. 24 degree

Step-by-step explanation:

Sides of the triangle are

a = 330 ft

b = 180 ft

c = 420 ft

From cosine rule we have

[tex]\angle A=\cos^{-1}(\dfrac{b^2+c^2-a^2}{2bc})\\ =\cos^{-1}(\dfrac{180^2+420^2-330^2}{2\times180\times 420})\\ =48.65^{\circ}[/tex]

[tex]\angle B=\cos^{-1}(\dfrac{a^2+c^2-b^2}{2ac})\\ =\cos^{-1}(\dfrac{330^2+420^2-180^2}{2\times 330\times 420})\\ =24.17^{\circ}[/tex]

[tex]\angle C=\cos^{-1}(\dfrac{a^2+b^2-c^2}{2ab})\\ =\cos^{-1}(\dfrac{330^2+180^2-420^2}{2\times 330\times 180})\\ =107.19^{\circ}[/tex]

The smallest angle in the triangle is [tex]\angle B=24.17^{\circ}[/tex].

a) Solve by determinant method: x - y = 2, 2x + 3y = 4​

Answers

Answer:

x = 2

y = 0

Step-by-step explanation:

x - y = 2

2x + 3y = 4

Using creamers rule of determinants, we have;

D =

|1 1|

|2 3|

Thus; D = (1 × 3) - (1 × 2)

D = 1

Dx =

|2 1|

|4 3|

Dx = (2 × 3) - (1 × 4)

Dx = 2

Dy =

|1 2|

|2 4|

Dy = (1 × 4) - (2 × 2)

Dy = 0

Thus;

x = Dx/D = 2/1

x = 2

y = Dy/D = 0/1

y = 0

IF THE RATIO IN A VALENTINE'S
DAY CANDY BOX OF MILK TO DARK
CHOCOLATES IS 23. HOW MANY
DARK CHOCOLATES ARE THERE IF
THERE ARE 8 MILK CHOCOLATES?

Answers

Answer:

12 dark chocolates

Step-by-step explanation:

Let there are 2x milk chocolates and 3x dark chocolates.

Total no of milk chocolates = 8

ATQ,

2x = 8

x = 4

Dark chocolates = 3x

= 3(4)

= 12

Hence, there are 12 dark chocolates.

How would you write the number displayed on the calculator screen in standard form

Answers

Answer:

E is short for 10^x. The number that comes after the E is the power of 10.

So its 7.6*10^12

now that scientifically notation

For standard your gonna need to simplify that

so we know 10^12 is 1000000000000

Multiply the 7.6

7600000000000

hope I helped :)

the length of a rectangle is 8 centimeters. what is the width?​

Answers

Answer:

This is a very vague question. We can't find out the width if it doesn't tell us the area. Comment on my answer the area and I can help.

HELP ILL GIVE BRAINLIEST AND THANKS
I think my teacher is sleep deprived
I have actually no idea how to do this- none of the answer choices seem to be correct or maybe i'm just... anyways help me!!!

Question: -4pv+ 9= -5
a.3.5
b. -14
c. -45

Answers

Answer:

B. -14

Step-by-step explanation:

sana maka tulong ako sayo

at ano ba ang grade nyo

what is the estimate of 29 x 688

Answers

Answer:

19952 :)

Step-by-step explanation:

Step-by-step explanation:

29 turns to 30

688 turns to 700

30×700=21000

Graph the solution set for the inequalíty
y> 2x-5 by following these steps:
Step 1: ldentify the slope and y-intercept.
slope = y-intercept =
Please help me

Answers

Answer:

Slope= 2

Y-intercept= -5

Step-by-step explanation:

This inequality is in slope-intercept form which means we can get both striaght from the inequaltiy. Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. In this inequality m would be 2 and b would be -5, so those are your answers.

ab and bc length and midpoint

Answers

Is there a picture of the figure?

(11/18-4/9)+1/6 pemdas fraction

Answers

Answer:

1/3

Step-by-step explanation:

11/18 - 4/9 + 1/6

= 1/6 + 1/6

= 1/3

The value of the fraction is 1/3.

What is PEMDAS Rule?

PEMDAS rule is the same as BODMAS rule.

PEMDAS is the abbreviation for Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction.

Given fraction is : (11/18 - 4/9) + 1/6

We have a parenthesis (brackets) in the given expression. First solve the operations inside the bracket.

And multiply the fraction 4/9 with 2 on both numerator and denominator.

(11/18 - 4/9) + 1/6 = (11/18 - 8/18) + 1/6

                           = 3/18 + 1/6

There is only an operation of addition left.

Multiplying both numerator and denominator of 1/6 with 3,

(11/18 - 4/9) + 1/6 = 3/18 + 3/18

                           = 6/18

                           = 1/3

Hence the value of the fractional expression given is 1/3.

Learn more about PEMDAS here :

https://brainly.com/question/29172059

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PLS HALP ASAP WILL GIVE BRAINLIEST FOR BEST ANSWER!!!

Steve set up a business making friendship bracelets. He earned $70 in January. He is projected to earn 120% more in February. How much is Steve projected to make in February? (1 point)

Question 30 options:

1)

$84

2)

$98

3)

$154

4)

$190

Answers

Answer:

70+120/100x70(1+100/100)=(100/100+120/100)= 220/100 hope helps you

Step-by-step explanation:

Answer:

154 dollary doooos

Step-by-step explanation:

In AABC, AB=8, BC=10, and AC=12. Let M, N, and K be the midpoints of the sides of AABC. Find length of each side of AMNK.​

Answers

Answer:

4,5,6

Step-by-step explanation:

A midsegment connects two midpoints, and this triangle would be made up of all midsegments.  If we know that midsegments are half of the side length, then we can get our answer.

1. A recipe calls for lb of flour for 1 batch. How many batches can be made with each of the following amounts? a. 1 lb b. lb c. lb

Answers

Each should be one batch. All three together would be 3.

Write the given linear system without the use of matrices. Assume X = x y z . X' = 7 6 −9 5 1 1 0 −3 4 X + 0 3 1 e6t − 8 0 4 e−3t

Answers

Answer:

X= 3

Step-by-step explanation:

3+x=x^2+3x Rewrite the equation by completing the square. What are the solutions to the equation?

Answers

Answer:

hope this helps

Step-by-step explanation:

3+x=x²+3x

Simply the equations.

= x+3=x²+3x

Subtract x²+3x from both sides.

x+3−(x²+3x)=x2+3x−(x²+3x)

−x2−2x+3=0

Factor left side of equation.

(−x+1)(x+3)=0

−x+1=0 or x+3=0

Answer:

x=1 or x=−3

PLS HELP FOR A GRADE DUE TODAY BRUH PLS

Answers

Answer:

A Yes, because every x-vaule has a single y-vaule

Step-by-step explanation:

None of the points share a point on the x axis meaning none of them are directly vertical of each other they are all seperate from each other.

Answer:

A

Step-by-step explanation:

Which graph represents the function fx) =|x–4?

Answers

The image below shows the graph f(x) = |x| – 4

Hope this helps! :)

If -1 2/3 is subtracted from 5 1/2, what will be the result?

a. negative
b. greater than 4
c. positive, but less than 4
d. equal to 4​

Answers

C    

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

When subtracting a negitive number from a positive number the difference ends up being a positive. The answer is 7, therefore, greater than 4.

Show that f '(x) = g'(x) for all x in their domains. Can we conclude from the corollary below that f − g is constant? If f '(x) = g'(x) for all x in an interval (a, b), then f − g is constant on (a, b); that is, f(x) = g(x) + c where c is a constant.

Answers

Answer:

Answer: 15 cm

Step-by-step explanation:

The derivative of a function at a point can be defined as its slope at that point. For f'(x) = g'(x) in the interval (a,b), it is proved that f - g is constant in (a,b).

What is a Derivative?

A derivative of a function is its rate change of increase or decrease in a given interval with respect to its variable. Derivative of a constant function is always zero.

Given that, f'(x) = g'(x) for all x.

Taking integral on both sides

f(x) + C₁ = g(x) + C₂

=> f(x) - g(x) = C₂ - C₁

=> f(x) - g(x) = C

Thus, f(x) - g(x) is constant is proved.

Similarly for interval an interval (a,b),

f(x) - g(x) = C

=> f(x)= g(x) + C

Hence, it is proved that in an interval (a,b), if  f'(x) = g'(x) then f(x)= g(x) + C.

To know more about Derivative click on the following link

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What angle would you use to represent 40 red cars out of 90 cars in total on a pie chart?​

. 40 degree
. 4 degree
. 160 degree
90 degree

Answers

Answer:

4

Step-by-step explanation:

i just know I took the test and I choose 90 and got it wrong

please HURRY IM ON A QUIZ

if 2 is substituted for x, which expression will NOT equal 5?

Answers

Answer:

It will be 2x -1

If x=2

2*2 - 1 = 4 - 1 = 3

Step-by-step explanation:

7 - x    If x=2

7 - 2 = 5

11 - 3x   If x=2

11 - 3*2 = 11 - 6 = 5

2x -1   If x=2

2*2 - 1 = 4 - 1 = 3

4x - 3    If x=2

4*2 - 3 = 8 - 3 = 5

Find an equation of the line that passes through the pair of points (-5, -9) and (2,-7)

Answers

Answer:

y=0.3x - 7.6

Step-by-step explanation:

line: y=ax+b

a= Δy ÷ Δx

a= (-9 + 7) ÷ (-5 - 2)

a= -2 ÷ -7 = approximately 0.3

y=0.3x + b

Now you can fill in one of the points to find b (or both to make sure you got the answer right).

0.3 × 2 + b = -7

0.6 + b = -7

b = -7 - 0.6 = approximately -7.6

So: an equation of the line that passes through this pair of points is y=0.3x - 7.6

On a test, i would write as many decimals as possible if not said not to, to get the most exact answer. Also remember to keep calculating with the number on your calculator and not to round them off for the most exact answer.

What is the product of 14/5

Answers

Answer:

2.8

Step-by-step explanation:

Just divide and get the answer

I NEED HELP ASAP PLEASE AND THANK YOU.

Answers

Answer:

C

Step-by-step explanation:

Happy Holidays ❄️☃️

What error did Wanda make?
None. Wanda’s work is correct.
Wanda converted the percent to a decimal incorrectly. It should be 0.073.
Wanda converted the percent to a decimal incorrectly. It should be 0.73.
Wanda has the wrong label. It should be hours, not dollars.

Answers

Answer:

C

Step-by-step explanation:

the guy above sucks

None. Wanda’s work is correct.

Wanda converted the percent to a decimal incorrectly. It should be 0.073.

Wanda converted the percent to a decimal incorrectly. It should be 0.73.

Wanda has the wrong label. It should be hours, not dollars.

Step-by-step explanation:

If Frank builds a concrete rectangular walkway that is 4 feet wide by 1.5 feet deep, by 20 feet long from the house to the storage shed, what is the volume of concrete used to pave the walkway?

Feet Cubed

Answers

Answer:

120 ft

Step-by-step explanation:

Please review the full explanation below

Answer:

........................................................................................

Step-by-step explanation:

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