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

Farid thinks last month was unusually rainy in his town—they had 6 inches of rain! His town's current record for rainfall in a year is 2 feet. Farid wonders what the new record would be if they were to keep getting this much rain for an entire year. If Farid's town had 6 inches of rain every month for 12 straight months, by how many feet would they beat the annual record?

Answers

They would beat the annual record by 4 feet

complete square to solve
3x^2 + 12x – 9 = 0

Answers

Answer: I hope this answer your question

Step-by-step explanation: Have a brilliant day mate- Lily ^_^

The area of triangle xyz is 35 cm. the height is 10cm. what is the base of the triangle?

Answers

Area of Triangle=1/2(h x b)
35=1/2(10 x b)
35=5 x b
35=5b
7cm=b is the base of the triangle

Answer:

Base of the triangle = 7 cm

Step-by-step explanation:

Given information,

→ Area of triangle = 35 cm

→ Height = 10 cm

Now we have to,

→ Find the base of the triangle.

Formula we use,

→ Area = ½ × b × h

Forming the equation,

→ (1/2) × b × 10 = 35

Then the value of b will be,

→ (1/2) × b × 10 = 35

→ (b × 10)/2 = 35

→ 10b/2 = 35

→ 10b = 35 × 2

→ 10b = 70

→ b = 70/10

→ [ b = 7 cm ]

Hence, the value of b is 7 cm.

Apply the power of a power property to simplify the expression (y^4/3 X y^2/3)^-1/2 = (^2)^-1/2

Answers

Answer: y= root 2, - root 2

Decimal form y= 1.41421356..., -1.41421356...

Answer:

1/y (c)

Step-by-step explanation: Don't listen to the other person he taking things but i promise you will get this right

Pleaseee helppp answer correctly !!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

84.8 ft

Step-by-step explanation:

6.6x6 + 8.2x2 + 2x2 + 12.4x2 = 84.8ft

Algebra 1B:
x/13 + 29 = -36​

Answers

Answer:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=−845

Step-by-step explanation:


what’s the answer? someone help!!!

Answers

I’m pretty sure it’s B
The answer is C am pretty sure

g(1) if g(x) = x^2 + 1.

Answers

Answer:

g(1)=2

Step-by-step explanation:

g(1)= 1^2+1 (you fill in 1 for x)

g(1)=1+1 (1 to the second power is 1 times 1 which is 1 and then you add 1 and 1)

g(1)=2

Parking lots A and B each charge a set fee for parking plus an hourly rate.

Hours Parked48Lot A Cost ($)19.00/33.00

Lot B Cost ($)20.00/32.00

How many more dollars does it cost per hour to park in Lot A than in Lot B? Give the answer as a decimal showing dollars and cents.

Answers

Answer:

$0.5

Step-by-step explanation:

Given :

Hours ___Lot A Cost ($) ___ Lot B Cost ($) 4____________19.00 _____ 20.00

8 ___________ 33.00 ______ 32.00

Using the equation :

y = mx + C

m = slope = Hourly charge

C = intercept = set park fee

m = y2 - y1 / x2 - x1

For LotA:

m1 = (33 - 19) / (8 - 4)

m1 = 14 / 4

m1 = 3.5

For LotB:

m2 = (32 - 20) / (8 - 4)

m2 = 12 / 4

m2 = 3

Since, m is the hourly cost :

Difference = m1 - m2

= 3.5 - 3

= $0. 5

If you flip the graph of the exponential function f(x) = 2x over the x-axis, what
is the equation of the new function?
O A. g(x) = 1/2
O B. g(x) = 2x - 1
O c. g(x) = 2-X
D. g(x) = -2X

Answers

Answer:

Step-by-step explanation:

G(x)=-2x

Answer:A

Step-by-step explanation:

Simplify :

3x - 2(x - 5)

Answers

Answer:

x + 10

Step-by-step explanation:

-2(x-5) =

-2x + 10

3x - 2x + 10 =

x + 10

:)

the answer should be x + 10 :)

The minute hand on MS. Scott’s clock is 22 inches long, from the center of the clock to its edge. Approximately how far does the minute hand travel around the clock in one hour?

Answers

Answer:

one thousand three hundred twenty inches

Help me please ❤️❤️❤️❤️, everyone I wil give u 10 points

Answers

in the box under the +4 put a +1, which means that column would equal 7. and then to the right of the +1 put a +6. on top of the +6 put a +3. then to the left of +3 put a 0. and the. on the bottom of the +1, right next to the +2, put a +6.

I NEED HELP THIS WORKSHEET IS DUE IN AN HOUR!!!!!!!!

14/15 + x = 4/9

Answers

Answer:

So let's rearrangeWe get x= -22/45

2x-2= 10x -4 help me

Answers

Answer

-8x=-2

x=-2/-8

x=1/4

Step-by-step explanation:

Look at the image of a composite figure. What polygon shapes form this
composite figure?

Answers

A triangle and a rectangle are combined to create the figure.

PLEASE HELP ME NOW 3/5g − 1/3 = −10/3 WHAT IS G

Answers

Answer:

The answer is G = -5

Step-by-step explanation:

your welcome :)

Find the x-and y-intercepts of the graph of 2x + 8y = 30. State your answers as
whole numbers or as improper fractions in simplest form.
It’s for algebra

Answers

Answer:

x int= (15, 0)

y int= (0, 15/4)

Step-by-step explanation:

for x int- plug 0 in for y and solve for x

for y int- plug 0 in for x and solve for y

Please help. I put a picture to make the question more clear.

Answers

Answer:

3/x+5

Step-by-step explanation:

4x+8/x^2+5x+6   x   3x+9/4x+20=

4(x+2)/x^2+3x+2x+6  x  3(x+3)/4(x+5)

reduce

x+2/x(x+3)(x+2)   x   3(x+3)/x+5

factor expression

x+2/(x+3)(x+2)  x  3(x+3)/x+5

reduce

3/x+5

3/x+5 is the answer to this question

Solve. Show all work.
40 = x - 10

Answers

Answer:

x=50

Step-by-step explanation:

40=x-10

Add 10 to both sides to isolate x

40+10=x

Solve.

50=x

Checking the solution

40=50-1040=40

Answer:

x = 50

Step-by-step explanation:

40 = x - 10

subtract/add (always do the opposite so we would add 10)

50 = x

there's your answer

can somebody answer it for me please. simplify and it can only contain positive exponent.

Answers

Answer:

1/2m^12

Step-by-step explanation:

simplify the expression :

m^-6/2m^3 x m^3

1/2m^9 x m^3

solution: 1/2m^12

sorry its really hard to explain the steps but I hope I helped you :)

Answer:

[tex]\frac{1 }{2m} ^x{12}[/tex]

Step-by-step explanation:

just take away the X

Juliette made cookies for a bake sale and wants to package the same number of cookies together. If she makes 16 chocolate chip cookies, 32 mint cookies, and 24 gingerbread cookies, what is the most number of each type of cookie that will be in the bag?

Answers

Answer:

8 cookies

Step-by-step explanation:

We are asked in the above question to find the most number of cookies that would be in the bag.

We solve the above question using the Greatest Common Factor method

We find the factors of 16, 24, 32

The factors of 16 are: 1, 2, 4, 8, 16

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 32 are: 1, 2, 4, 8, 16, 32

Then the greatest common factor is 8.

Therefore, the most number of each type of cookie that will be in the bag is 8 cookies

GEOMETRY: Find JL of the line.

Answers

Answer:

JL = 31

Step-by-step explanation:

JL is the total length of the line segment. We know that JK is 15 units long and that KL is 16 units long. So, you would add these numbers (15 & 16) together to get the total length of the line segment. Hope this helps! :)

Can any two Isosceles triangles always be SIMILAR to each other ?

true or false

Answers

False it is not similar same thing

Answer:

False. An isosceles triangle has at least 2 equal legs. The third leg can vary in length.

Step-by-step explanation:

1.Construct a linear equation from the following statements.

(i) The quotient of three times a number and 5 is 9.
(ii) One-third a number added to 5 gives 25.

2. Solve the following equations.

15(x-1) – 3(x-2) + 7(x+3) = 0

3. What do you mean by SAS and RHS?

4. Find whether the pairs of triangles in each question below are congruent or not. If yes then state the criterion of congruence in each case.


P Q
_________
| |
3cm | | 3cm
|_________|
S R​

Answers

Answer:

Stop cheating!!!!!

6/12x - 10 = 30 solve for x

Answers

Answer:

x = 80

Step-by-step explanation:

(6/12)*x-10 = 30 // - 30

(6/12)*x-30-10 = 0

1/2*x-40 = 0 // + 40

1/2*x = 40 // : 1/2

x = 40/1/2

x = 80

Hi there!

x=80

1.Multiply the terms:

[tex]\frac{6}{12}[/tex]·[tex]80=\frac{480}{12}[/tex]

2.Divide the fraction term:

[tex]\frac{480}{12}=40[/tex]

3.Subtract the two terms:

[tex]40-10=30[/tex]

This means, x=80..

If 2^2x = 2^3, what is the value of x?

Answers

Answer:

X = 3/2.

Step-by-step explanation:

Please refer to the attachment given above.

The value of x in the equation 2[tex]^{(2x)}[/tex] = 2³ is 1.5.

To find the value of x in the equation 2[tex]^{(2x)}[/tex] = 2³, we can use the property of exponents that states: If two exponential expressions have the same base and are equal, then their exponents must be equal.

In this case, we have 2[tex]^{(2x)}[/tex] = 2³. Since the bases are the same (both are 2), we can equate the exponents:

2x = 3

Now, to solve for x, divide both sides by 2:

x = 3/2

So, the value of x is 3/2 or 1.5.

To know more about equation

https://brainly.com/question/29174899

#SPJ2

you can buy 7 oranges for 8.50 what is the price per orange

Answers

Answer:

The price of one orande is 1.21.

Step-by-step explanation:

Answer:

Short Version: 1.21

Long Version: 1.21428571

Step-by-step explanation:

Just divide 8.50 by 7

Lily begins solving the equation 4(x-1)-x=3(x+5)-11. Her work is shown below. 4(x-1) - x = 3 (x+5)-11 4x −4) −x =3x +15 −11 3x-4= 3x+4 How can her solution be interpreted? The equation has no solution The equation has one solution: x=0x=0. The equation has infinitely many solutions. The equation has one solution: x=8x=8.

Answers

Answer:

Um...

Step-by-step explanation:

Hai

Mel uses one fourth of a yard of ribbon to make a hair bow how many hair bows can mel make with 1 yard of ribbon​

Answers

Answer:

4 hair bow

Step-by-step explanation:

if 1/4 can make 1 hair bows you can make 4 hair bows

, it's simple 4/1=4

Answer:

4 ribbons as 1/4 is used to make one so an entire yard can be used to make  4

this can be prooved by using division

1÷1/4

making their  denominators equal

=(1/1*4)÷(1/4*1)

=4/4÷1/4

=4

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