Harvey is studying the polynomial f(x) = (2x - 3)(x - 4)(x2 + 3) and determines that the polynomial has four real roots. Is
Harvey's statement CORRECT?
A. No, the polynomial f(x) has 2 real roots and 2 complex roots when solved.
O B. Yes, the polynomial f(x) has 4 x-intercepts so the function has 4 real roots.
C. Yes, the polynomial f(x) has a degree of 4 so the function has 4 real roots.
OD. No, the polynomial f(x) has 3 real roots because there are 3 factors.

Answers

Answer 1

Answer:

It is A, I highly suggest you should read my explanation.

Step-by-step explanation:

(2x - 3)(x - 4)(x^2 + 3)

Exponent of 2x = 1

Exponent of x = 1

Exponent of x^2 = 2

Add them all together to get the degree. 1 + 1 + 2 = 4

Now we can tell that the polynomial can have 1,2,3,4, or no roots at all. The max number roots it can have is 4

To see the number of roots it has, we have to set each part equal to 0

2x - 3 = 0

Add 3 to both sides

2x - 3 + 3 = 0 + 3

2x = 3

Divide both sides by 2

2x/2 = 3/2

x = 3/2 or 1.5

Next,

x - 4 = 0

Add four to both sides

x - 4 + 4 = 0 + 4

x = 4

Then,

x^2 + 3 = 0

Subtract 3 from both sides

x^2 + 3 - 3 = 0 - 3

x^2 = -3

Find the square root of both sides

sqrt(x^2) = sqrt(-3)

x = i*sqrt(3), -i*sqrt(3)

Those are imaginary numbers, therefore there are not real.

The real roots are x = 3/2, 4

Harvey stated that this equation has four real roots. We can cross options B and C out since they stated he was correct.

It is not D because finding a square root of a number gives two answers; the positive and negative version, so it will have two solutions. There were only two real roots and the other two roots are complex roots.

That leaves us to option A, which states that there are 2 real and 2 complex roots. It is correct


Related Questions

The graph shows the number of points, y, a player earns in a balloon game
based on the number of balloons popped, X.

Answers

y = 25x
Slope is rise over run or (y2-y1)/(x2-x1)
(25-0)/(1-0)=25
No b value in y=mx+b because the origin is at 0.

if are is 24cm² find the x ​

Answers

Answer:

[tex]x = 6[/tex]

Explanation:

Given:

[tex]Area = 24cm^2[/tex]

See attachment for shape

Required

Find x

The attached shape is a rectangle.

So:

[tex]x * 4 = 24[/tex]

[tex]4x = 24[/tex]

Divide both sides by 4

[tex]\frac{4x}{4} = \frac{24}{4}[/tex]

[tex]x = \frac{24}{4}[/tex]

[tex]x = 6[/tex]

20 is what. % more than 5

Answers

Answer:

400%

Step-by-step explanation:

20 divided by 5 = 4

100 times 4 = 400

Find the solution
4y-x=5+2y
3x+7y=24

Answers

Answer:

24

Step-by-step explanation:

Linda made $270 for 18 hours of work.
At the same rate, how much would she make for 7 hours of work?
$

Answers

Answer:

105

Step-by-step explanation:

so you divide 270 by 18 hours to get 15 , so she gets paid £15 every hour

you times 15 by 7 = 105

Answer:

Linda would make $105 for 7 hours of work, she made the same amout of money per hour.

Step-by-step explanation:

270/18=15

15 x 7= 105

There are five trees per square mile. Linda cuts down every tree in a 6
mile by 4 mile area.
How many trees did Linda cut down?

Answers

Answer:

3 trees and a square mile takes 1 tree

Step-by-step explanation:

a square mile means 2 miles each

Answer:

120

Step-by-step explanation:

Length=6

Width=4

L×W=A

6×4=24

A× (amount of trees in a square mile) =Ans.

24×5=120

#gamer

please help me on this will give you brainliest!!

Answers

36!!
18/2= 9
45/5= 9
9 x 4 = 36

Answer:

AC = 36

Step-by-step explanation:

since these triangles are similar, we can use the triangle similitary theorem. This means that the sides are proportional to each other.

ef/bc = 5/45 (1/9) = ed/ba =  2/18 (1/9)

we can see the sides are in a ratio of 1:9, and plug it in the proportion

df/ac = 1/9

4/ac = 1/9

cross multiply and we get that ac = 36

What is the length of segment AB?

Answers

Answer:

Option 1

Step-by-step explanation:

Use Pythagorean theorem,

AB² = base² + altitude²

      = 7² + 6²

     = 49 + 36

     = 85

AB =√85

Answer:

option a.

6²+7²=ab²(by Pythagoras theorem)

36+49=ab²

85=ab²

square root 85=ab

At 10 AM, one share of Starbucks stock was $35. By 2 PM the price was $41. The rate the Starbucks stock value was changing is - per hour

Answers

Answer:

1.50$

Step-by-step explanation:

difference in money amount: $6

difference in hours: 4

6 divided by 4 equals 1.50.

1.50 times 4 equals 6, hence its 1.50 per hour.

The rate of change in the Starbucks stock value is 150%.

Given that, At 10 AM, one share of Starbucks stock was $35. By 2 PM the price was $41.

We need to find the rate the Starbucks stock value was changing is - per hour.

What is the rate of change?

A rate of change is a rate that describes how one quantity changes in relation to another quantity.

Now, the difference in money=41-35=$6

The number of hours between 10 AM to 2 PM is 4 hours.

The rate of change = The difference in money/Number of hours × 100

=6/4 × 100

=150%

Therefore, the rate of change in the Starbucks stock value is 150%.

To learn more about the rate of change visit:

https://brainly.com/question/12786410.

#SPJ2

Plz help me plz
Also phone reval XD

Answers

Answer:

5.50

Step-by-step explanation:

5 = whole number

.

5 = Tenths

0 = Hundreths

5.50

Hope this Helps!
It would be 5.50 5 is the tenths and zero is the hundredth

Over a 30-day period, the mean temperature in Morristown was 56°F with a standard deviation of 8.4°F and the mean temperature in San Juan was 67°F with a standard deviation of 1.5°F.

What statement best describes the data?


The temperatures were of similar consistency in Morristown and San Juan.

The temperatures were more consistent in Morristown.

The temperatures were more consistent in San Juan.

Answers

Answer: i think the answer would be d the temperatures were more consistent in san juan im pretty sure

Step-by-step explanation:

hope this helped im pretty sure this is right check my yt channel out hailey azbell

A laptop computer is normally $1300 but is discounted to $988. What percent of the original price does Charles pay?

Answers

Answer:

Step-by-step explanation:

Your answer

24% discount.

Pays a total of 76 % cost

Mark it as Brainlist. Follow me for more answer.

Write an expression, in its simplest form, for the volume of this cuboid:

Answers

Answer:

volume of cuboid=l×b×h

=2x+7+x+5

Answer:

volume of cuboid= l×b×h=(2x+7)x×5=5x×2x+5x×7

=10x²+35x

A TV has a length of 68 inches and a height of 51
inches. When TV's are advertised the size listed is the
diagonal length. What would be the advertised size of
this TV?

Answers

Answer:

85 inches

Step-by-step explanation:

Using pythag.  A^2 + B^2 = C^2  

(68*68) + (51*51) = 7225^2

Thus if you square root 7225, you get your answer - 85 inches.

How many solutions does the equation have? -10(x - 1) = 10 - 10x *

O Zero Solutions
O 1 Solution
O Infinite Solutions​

Answers

Answer:

infinite

Step-by-step explanation:

it results in 10-10x=10-10x if you simplify

can also be simplified more into x=x

but we already know x has to equal x.

factorise x^12 y^4 - x^4 y^12

PLEASE PLEASE explain in step by step Pleasseeeeee​

Answers

Answer:

Step-by-step explanation:

First, look at your terms. You have two terms and two variables in each. So they can be factored out because you can distribute them back in easily.

Focus one variable first, x. You cant factor an x^12 out of an x^4. You can, but you really don't want to, it'll turn your problem into a mess. So the only thing you can do is factor out the lower exponent, x^4.

[tex]x^4(x^8y^4-y^1^2)[/tex]

We arent done yet because the terms still share the y variable. You cant factor a y^12 from a y^4. This is the same problem with the x variable. So take out the lower one, y^4.

[tex]x^4y^4(x^8-y^8)[/tex]

Please help!!!! The roots of x^2-2x-2=0 are A.1+square root of 3 B.1+square root of 12 or C.No real roots

Answers

Answer:

A

Step-by-step explanation:

We have the equation:

[tex]x^2-2x-2=0[/tex]

We can use the quadratic formula. In this case, a = 1, b = -2, and c = -2. Hence:

[tex]\displaystyle x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-2)}}{2(1)}[/tex]

Evaluate:

[tex]\displaystyle x=\frac{2\pm\sqrt{12}}{2}[/tex]

Simplify:

[tex]\sqrt{12}=\sqrt{4}\cdot\sqrt{3}=2\sqrt{3}[/tex]

Hence:

[tex]\displaystyle x=\frac{2\pm2\sqrt{3}}{2}[/tex]

Divide:

[tex]x=1\pm\sqrt3[/tex]

The correct answer is A.

what is the simplest from of this expression? (-3x^2 + 4x) + (2x^2 - x -11)
A. -x^2 + 3x + 11
B. -x^2 + 5x - 11
C. -x^2 + 5x + 11
D. -x^2 + 3x - 11​

Answers

Answer:

D

Step-by-step explanation:

Can someone help please

Answers

Answer:

YES

Step-by-step explanation:

Please help solve the problem below.

Answers

Answer:

1. x = 2

2. x = 5

3. x = 8

4. x = 28

5. x = 13

6. x = 11

7. x = 0

8. x = 72

9. x = 6

10. x = 38

Step-by-step explanation:

hope that helps!

1. subtract 6 on both sides

2. add 3 on both sides

3. divide both sides by 2

4. multiply both sides by 2

5. add 8 on both sides

6. subtract 9 on both sides

7. add 5 on both sides

8. multiply both sides by 6

9. divide both sides by 4

10. add 18 on both sides

14. AMKL is an isosceles triangle with MK ML.If MK = 7x - 15, KL = 4x - 6, and ML = 10X - 12, find x and the measure of each side.​

Answers

Answer:

You can do it! Sorry i can't help because your on a different level. Try your best!

Step-by-step explanation:

PLS HELP!!! WILL GIVE BRAINLIEST IF CORRECT!!!

Answers

Answer:

Scale factor 3

Step-by-step explanation:

The rectangle is enlarged by a scale factor of 5. What is the new
measurement of the longest side?

Answers

Answer:

25 I'm pretty sure

Step-by-step explanation:

5×5=25

Answer:

25 cm

Step-by-step explanation:

If it is enlarged by the scale factor of 5, you are multiplying by 5. 5 cm is the longest side, so therefore 5 cm times 5 cm is equal to 25.

3² • 9³ = [ ]
solve ​

Answers

Answer:

3⁸ or 6561

Step-by-step explanation:

First, let's look at PEMDAS - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

There are no parentheses, so let's solve the exponents.

3² • 9³

3² = 9

9³ = 729

Your expression is:

9 • 729

Now let's multiply.

= 6561

This number can also be expressed with exponents.

Since 9 = 3², 9³ = 3²⁽³⁾

Now your expression is:

3² • 3²⁽³⁾

First, solve the exponents by multiplying.

3² • 3⁶

When you multiply two expressions with exponents that have the same base (3), you add the exponents.

3² • 3⁶ = 3⁽²⁺⁶⁾ = 3⁸

3⁸ also equals  6561.

Your answer is 3⁸ or 6561.

Hope this helps!

A line with a slope of 2 passes through the point (5, 8). What is its equation in slope-intercept form? (I will make u brainleist)

Answers

Answer:

y= 2x -2

Step-by-step explanation:

I need some help on this question! I will mark you if you answer.

Answers

Answer:

definitely 145

Step-by-step explanation:

It is 145 degrees I hope this helps :)

NEEEED HELP!!!!!!!!!

Answers

Answer:

1/3 is your awnser also what ur name in prodigy ill play with u im level 100

Step-by-step explanation:

Answer:

[tex] \frac{2}{5} + \: x = \frac{11}{15} [/tex]

5.3=15

2.3=6

[tex] \frac{6}{15} + \frac{5}{15} [/tex]

What is the equation, in point-slope form, of the line passing through the point (8, -3) with a slope of 5?

Answers

The answer would be ~y+3=5(x-8)~

Hope this helps

Have a great day/night

Pleaseee help answer correctly !!!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!

Answers

Answer:

108º

Step-by-step explanation:

to find the sum of interior angles: ( n − 2 ) × 180 = x

x = 540º

n = # of interior angles

first, solve for n

(n - 2) • 180 = 540                        distribute to 180 to (n - 2)

180n - 360 = 540                         add 360 to both sides

180n = 900                                  divide both sides by 180

n = 5

to find measure of each angle:

540 ÷ 5 = 108º

Please pleaseeee help!
Im so lost this is the last question i have and I’ve been working on it forever. Even asked my mom and she had no idea! Helpp please!!

Answers

Answer:

Remember that the roots are the values of the variable when the expression equals 0.

a: 4 + 3 = 7 and 4*3 = 12 so we have (x + 3)(x + 4) with roots -3, -4

b: -4 + -2 = -6 and -4*-2=8 so we have (t-2)(t-4) with roots 2, 4

c: 2*-4 + 6 = -2 and -4*6=24 so we have (2n+6)(n-4) with roots -3, 4

d: -7+-4 = -11 and -7*-4=28 so we have (y-4)(y-7) with roots 4, 7

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