How many real roots does the polynomial 2x^3+8x-7 have?

Answers

Answer 1
One.

And you don’t need to calculate them to know that.

First, you know that polynomials of grade three have either one or three real roots. Second, you know that to have three real roots, they have to have a local maximum and a local minimum.

Take the derivative of your polynomial

()′()=23+8−7=62+8 f(x) =2
x
3
+8x−7
f

(x) =6
x
2
+8

Find the possible zeros of the derivative

′()=62+8=0
f

(
x
)
=
6
x
2
+
8
=
0

and see that there are no real zeros of the derivative. So the polynomial has no local maxima or minima, so it has exactly one real zero.

For the same reason every polynomial of the form

3++
a
x
3
+
b
x
+
c

with ,>0
a
,
b
>
0
has exactly one real root

15



2


Related Questions

How do you do this, because I really do not know how to do this and plz explain how to do this

Answers

Answer:

A

Step-by-step explanation:

the leading degree(the biggest power in the function) x^4 and the leading coefficient is the number next to the highest power which is -5

so the answer should be

-5,4,x -> infinity, f(x) -> -infinity ; x -> -infinity, f(x) -> -infinity    

when you get asked questions like this look for the biggest power and the number next to it. if the power is even x will always be positive if its odd x can be either positive or negative it depends on restrictions.

for instance in this example -5 * x^4 will always give you negative because -5 will multiply with a positive number x (the power is even so its always positive)

if there was 200 kids= 100% and 43 of them left what is the percent

Answers

Answer:

It would be 86 as 43% of 200 is 86

Step-by-step explanation:

Solve the math problem

Answers

Answer:

2) a.   slope = 4/3

2) b.   slope = -4

Step-by-step explanation:

The slope of the line that passes through points

[tex] (x_1, y_1) [/tex]  and  [tex] (x_2, y_2) [/tex]

is m, given by the slope formula below:

[tex] m = \dfrac{y_1 - y_2}{x_2 - x_1} [/tex]

2) a. (30, 32) and (18, 16)

[tex] m = \dfrac{y_1 - y_2}{x_2 - x_1} [/tex]

[tex] m = \dfrac{32 - 16}{30 - 18} [/tex]

[tex] m = \dfrac{16}{12} [/tex]

[tex] m = \dfrac{4}{3} [/tex]

2) b. (4, -26) and (10, -50)

[tex] m = \dfrac{y_1 - y_2}{x_2 - x_1} [/tex]

[tex] m = \dfrac{-50 - (-26)}{10 - 4} [/tex]

[tex] m = \dfrac{-24}{6} [/tex]

[tex] m = -4 [/tex]

0.1 x 0.01 x 0.001
ans ???

Answers

>> Answer

________

[tex] \: [/tex]

[tex]0.1 \times 0.01 \times 0.001 = ...[/tex]

[tex] = \frac{1}{10} \times \frac{1}{100} \times \frac{1}{1.000} [/tex]

[tex] = \frac{1}{10 \times 100 \times 1.000} [/tex]

[tex] = \bold{ \frac{1}{1.000.000}} [/tex]

Answer:

[tex]0.1 \times 0.01 \times 0.001 = 0.000001 \\ \\ \\ \\ i \: hope \: it \: is \: helpfull[/tex]

Sam practiced his long jump in P. E. On his first attempt, he jumped 1 meter 47 centimeters. On his second attempt, he jumped 98 centimeters. How much farther did Sam jump on his first attempt than his second?.

Answers

Answer:

51

Step-by-step explanation:

98-47= 51

im bo.red so there ya go

Write the following equation in the general form Ax + By + C = 0.

1/2 y - 1/3x - 1 = 0

-2x + 3y - 6 = 0
2x - 3y - 6 = 0
2x - 3y + 6 = 0

Answers

The answer is the second option.

To find the answer quickly, fist look at the signs associated with the terms. The is a negative sign with the B and C in the original equation, and the second option is the only one that follows that.

You use 6 as the C since that is a shared value when multiplying 2 and 3, so 1/2 becomes 2 and 1/3 becomes 3.

Please help, thank you (NO LINKS!)
Patsy has cheerleading practice every fourth day. She wants to be in the school play, but they have practice every sixth day. If both start on September 5th, what would be the next date she has to choose between cheerleading and play practice? Show your work and explain.

Answers

Answer:

the first time 4 and 6 intersent is 24

so 24 days after september 5th

september 29th

Hope This Helps!!!

Find the value if f(x) = -3x - 8 and g(x) = x2 + 3. Find the value g(-5) =​

Answers

Step-by-step explanation:

g(x) = x² + 3

g(-5) = (-5)² + 3

g(-5) = 25 + 3

g(-5) = 28

What is the product?

(4y − 3)(2y2 + 3y − 5)

8y3 + 3y + 15
8y3 − 23y + 15
8y3 − 6y2 − 17y + 15
8y3 + 6y2 − 29y + 15

Answers

Answer:

the last one

Step-by-step explanation:

Which equation goes through the points (-3,5) and (-1,7)?

Answers

Answer:

y=x+8

Step-by-step explanation:

slope = y2-y1/x2-x1

slope = 7-5/-1+3

slope = 2/2

slope = 1

y=x+b

7=1(-1)+b

7=-1+b

b=8

y=x+8

What is the first step in solving this equation?
3(2x + 6) - 4x = 2(5x - 2) + 6
Use the subtraction property of equality to subtract 6 from both sides.
Use the addition property of equality to add 4x to both sides.
Combine the like terms on each side of the equation.
O Use the distributive property on each side of the equation.

Answers

Answer: use distributive property

Step-by-step explanation:

you must always start from the numbers in the parentheses

Find the value of y to the nearest tenth.

Answers

Step-by-step explanation:

the easiest approach seems to be the law of sines :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides and the angles are always opposite of each other.

we have here a right-angled triangle, so the angle opposite of 10 is 90 degrees.

10/sin(90) = 10/1 = 10 = y/sin(37)

y = 10×sin(37) = 6.018150232 ≈ 6.0

the first shower head was used 20 gallons of water in 5 minutes. How many gallons of water will we use in one minute?​

Answers

Answer:

4

Step-by-step explanation:

because since it says 5 minutes

and. 5×4=20 so 4 gallons of water in 1 minute

What is the value of X?

Answers

Answer:

45 i think

if not 54

I'm pretty sure it's 45

hope this helped :)

Solve the equation: [tex]x^{2} +5x+6=0[/tex]
I know [tex]x^{2} +5x+6=(x+3)(x+2)[/tex] (that was part a) but I don't know where to go from here!

Answers

Step-by-step explanation:

but then you did already the most work.

because just think : when is the expression

(x+3)(x+2) equal to 0 ?

only, if at least one factor of the multiplication is equal to 0.

you know, for example, 5×0 = 0, or 0×3 = 0.

that means either (x+3) or (x+2) must be 0.

x + 3 = 0

x = -3

and

x + 2 = 0

x = -2

and there you have it.

a quadratic equation (with the highest x exponent is 2) has 2 solutions for being 0.

and this one here has the 2 solutions

x = -3 and

x = -2

again, by finding the factors you did already the biggest and most difficult part yourself. congratulations !

What is the missing step in solving the inequality 5 – 8x < 2x + 3?

Add 2x to both sides of the inequality.
Subtract 8x from both sides of the inequality.
Subtract 2x from both sides of the inequality.
Add 8x to both sides of the inequality.

Answers

Answer:

Add 8x to both sides of the inequality.

Step-by-step explanation:



Maricopa's Success scholarship fund receives a gift of $ 115000. The money is invested in stocks,

bonds, and CDs. CDs pay 4 % Interest, bonds pay 5.3 % interest, and stocks pay 6.2 % interest.

Maricopa Success Invests $ 15000 more in bonds than in CDs. If the annual income from the

Investments is $ 6220, how much was invested in each account?

Maricopa Success invested $

in stocks.

Maricopa Success invested $

in bonds.

Maricopa Success invested $

in CDs.

Answers

Answer:

  $50,000 in stocks

  $40,000 in bonds

  $25,000 in CDs

Step-by-step explanation:

Let c represent the amount invested in CDs. Then the amount invested in bonds is (c+15000) and the amount invested in stocks is (115000 -c -(c+15000)) = (100000 -2c). The total interest earned is ...

  0.04c +0.053(c +15000) +0.062(100,000 -2c) = 6220

  -0.031c +795 +6200 = 6220

  -0.031c = -775 . . . . . . . . . . . . . . . subtract the left-side constants

  c = 25000 . . . . . . . . . . divide by the coefficient of c

  c+15000 = 40000 . . . . bonds

  100000 -2c = 50000 . . . . . stocks

Maricopa Success invested ...

  $50,000 in stocks

  $40,000 in bonds

  $25,000 in CDs

ILLA
2. Miles makes $14 per hour but has to pay $55 for his cell
phone bill.

Answers

miles had to work 4 hours to pay his phone bills and he had 1$ left over

Answer:

i dont know

Step-by-step explanation:

what question are you asking?

The functions r and s are defined as follows.
r(x) = -x +1
s(x)=2x2-1
Find the value of r(s(4)).
numeral composition of functions

Answers

Answer:

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

It took Jason 20 days to write his college essay. He wrote half a page (0.5) every day. How long was the report?I need an explanation to so I can understand, thank you!

Answers

The report was 10 pages. This is because we know that Jason wrote half a page a day, and if he consistently wrote each day and I took him a total of 20 days to finish, all you would have to do is multiply 20 by .5 (half a page), you would then get 10, which means that in 20 days he wrote 10 pages

Algebra 2 please help

Answers

Answer:

4th option

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 4x² - 5x + 8 +2x² + x - 2 ← collect like terms

= 6x² - 4x + 6

The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120.

a. Find some possible combinations of 2-seat tables and 4-seat tables that will seat 120 customers.

Answers

Answer:

5 points for what

Step-by-step explanation:

HeY

-15 < x - 8 < -4

SOLVE COMPUND INEQUALITY​

Answers

[tex] \sf \: -15 < x - 8 < -4 [/tex]

Add 8 to all parts

[tex]\sf \longmapsto−15+8<x−8+8<−4+8[/tex]

[tex]\sf \longmapsto−7<x<4[/tex]

[tex] \boxed{\sf−7<x<4 }[/tex]

Graph attached

3x^3 -5x^2 -x+3 when x=4 help I'm stuck on this

Answers

The value of the expression [tex]3x^3-5x^2-x+3[/tex] when x = 4 is 110

The given equation is:

[tex]3x^3-5x^2-x+3[/tex]

To find the value of [tex]3x^3-5x^2-x+3[/tex] when x = 4, substitute x = 4 into the expression [tex]3x^3-5x^2-x+3[/tex]

When x = 4:

[tex]3x^3-5x^2-x+3 = 3(4^3)-5(4^2)-5+3\\\\3x^3-5x^2-x+3 =3(64)-5(16)-2\\\\3x^3-5x^2-x+3 =192-80-2\\\\3x^3-5x^2-x+3 =110[/tex]

Therefore, the value of the expression [tex]3x^3-5x^2-x+3[/tex] when x = 4 is 110

Learn more here: https://brainly.com/question/25691329

i forgot how to turn fractions into decimals pls help me

3/5 = 0.6 but how do u get 0.6

pls show the work

Answers

Answer:

A fraction is essentially division, so 3/5 is the same as 3 ÷ 5

3÷5 = 0.6

[tex]5\sqrt{3\\[/tex]

(imagine the square root is the divsion thing)

5 cannot go into 3 so the answer is a decimal

then add a zero at the end of 3 to make 30

   0.

[tex]5\sqrt{30[/tex]

and 5 can go into 30, 6 times so you add a 6 to make 0.6

    0.6

[tex]5\sqrt{30[/tex]

Which of the following is a solution to the inequality below?19 ≥ 5k + 6

Answers

Answer:

k ≥ 13/5 or k ≥ 2.6 ( same thing )

Step-by-step explanation:

symbol stays the same throughout (≥)

subtract 6 from both sides of the symbol ( 13 ≥ 5k)

divide both sides by 5 (13/5  ≥ k )

your answer can be written as k ≥ 13/5 or k ≥ 2.6

Please help meeeeeeeeeeeeee

Answers

Answer:

-47

Step-by-step explanation:

First term in the sequence is given as 30. The common difference (difference between first term and next term) is -7. Since we are looking for the 12th term we can do 30 - (11 * -7) = -47. It's 11 * -7 because we already are given one term in the problem statement.

if 20 articles cost $90,then the cost of 9 articles is

Answers

Answer:

$40.50

Step-by-step explanation:

90 divided by 20 is 4.5. then you multiply that times 9 and that's your answer.  

The height of a tree is 8.2 meters.
What is the tree's height in centimeters?

Answers

Answer:

820 centimeter :3

Step-by-step explanation:

8.2 meters

move the decimal back twice because of KiloHecaDecaBase (m,l,g)DeciCentiMilli

As we know 1 meter is equal to 100 centimeters so the height of the tree 8.2 meters is equal to 820 meters

What is unit conversion?

The same attribute is expressed using a unit conversion but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.

Measurements are frequently offered in one set of units, like feet, but are required in another set, like chains.

A conversion factor is a mathematical equation that facilitates an equal exchange of feet for chains.

Given, The height of a tree is 8.2 meters, now we know 1 meter is equal to 100cm so to convert some quantity from meters to centimeters we multiply by 100.

∴ 8.2 meters is equal to (8.2×100) = 820 centimeters.

learn more about unit conversion here :

https://brainly.com/question/11543684

#SPJ5

i will give crown if answered right i just need to check my work

Answers

Answer:

9x(3x-2) (3x+2)

Step-by-step explanation:

[tex]81x^{3}-36x[/tex]

9(9x³ - 4x)

9x(9x² - 4)

Since both terms are perfect squares factor using the difference of squares formula,  a² - b² = (a + b) (a - b)

Therefore, 9x(3x-2) (3x+2)

Answer:

81z^3-36z = 9z(3z-2)(3z+2)

Step-by-step explanation:

(81z^3-36z)=9z(9z^2-4)

9z(9z^2-4)=9z(3z-2)(3z+2)

81z^3-36z=9z(3z-2)(3z+2)

81z^3-36z=9z(3z-2)(3z+2)

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