Consider the function f(x) = x^3 - 7x^2 - 2x + 14
What is the total number of zeros of f(x)? Explain how you got your answer.
Find the zeros of f(x). Explain your procedure as you solved it.

Answers

Answer 1

Answer:

There are 3 zeros, which are:

[tex]x=7,\:x=-\sqrt{2},\:x=\sqrt{2}[/tex]

Step-by-step explanation:

Given the function

[tex]f\left(x\right)\:=\:x^3\:-\:7x^2\:-\:2x\:+\:14[/tex]

To get the zeros of [tex]f(x)[/tex], set [tex]y[/tex] or [tex]f(x) =0[/tex]

so

[tex]0=x^3-7x^2-2x+14[/tex]

as

[tex]x^3\:-\:7x^2\:-\:2x\:+\:14=\left(x-7\right)\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)[/tex]

so

[tex]\left(x-7\right)\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)=0[/tex]

Using the zero factor principle:

[tex]\mathrm{ \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]

so

[tex]x-7=0\quad \mathrm{or}\quad \:x+\sqrt{2}=0\quad \mathrm{or}\quad \:x-\sqrt{2}=0[/tex]

solving

[tex]x-7=0[/tex]

[tex]x=7[/tex]

[tex]x+\sqrt{2}=0[/tex]

[tex]x=-\sqrt{2}[/tex]

[tex]x-\sqrt{2}=0[/tex]

[tex]x=\sqrt{2}[/tex]

Therefore, there are 3 zeros, which are:

[tex]x=7,\:x=-\sqrt{2},\:x=\sqrt{2}[/tex]


Related Questions

There are 25 servings in a 16.8 ounce bottle of
cooking oil. How many ounces
are in a serving?

Answers

0.672 is the correct answer

Can somebody plz help me with this question!

Answers

Answer:

y= -4/5x - 2

Step-by-step explanation:

y=mx+b thats all i can think of to put here lol

have a good day lovely =)

General admission to Paul’s Pumpkin Patch is $8.00. For children to ride the various rides, they must use tickets that cost $1.00 each. The number of tickets needed for each ride varies. The function for this situation is P(x) = x + 8, where P(x) represents total cost as a function of the number of tickets, x. What is the domain for visiting and riding rides at Paul’s Pumpkin Patch?
A. P(x) ≥ $8.00
B. x is all real numbers
C. x ≥ 0, where x is non-negative
D. x ≥ 0, x is an integer

Answers

Given:

Total cost P(x) as a function of the number of tickets, x is

[tex]P(x)=x+8[/tex]

To find:

The domain for visiting and riding rides at Paul’s Pumpkin Patch.

Solution:

Domain is the set of input values.

Here, domain is x and it represents the number of tickets.

We know that, number of tickets cannot be negative or decimal or fraction vales. So, x must be non-negative and integer value.

Domain = x ≥ 0, x is an integer

Therefore, the correct option is D.

PLEEAAASEEEE can anyone explain how I do this? Or does anyone have the answer??

Answers

Answer:

I am fairly certain is y=8x

Step-by-step explanation:

The only definitive points are (0,0) and (10,80)

So using the slope formula rise/run i got 8

Which inequality represents the range of the relation graphed below?

Answers

Answer: I think it’s d

Step-by-step explanation:

What is f(x)= 3x+ 13(17x-7) if x equals 4?

Answers

The answer to this is 805

Answer:

805

Given:

x=4

Step-by-step explanation:

f(x) = 3x + 13(17x-7)

f(x) = 3 × 4 + 13(17 × 4 - 7)

f(x) = 12 + 13(68 - 7)

f(x) = 12 + 13 × 68 - 13 × 7

f(x) = 12 + 884 - 91

f(x) = 12 + 793

f(x) = 805

hope you understood❤❤

Using coupons you spell $91 grocery shopping this is 65% of the total retail price of groceries how much would you have spent if you had not use the coupons

Answers

$140 because

$91 divided by 65 is 1.4
1.4 times 100 is 140

Find each percent increase. Round to the nearest percent.

From 5 miles to 16 miles

Answers

love the saiki k pfp, also the answer to your question is...

answer: 11 since its from 5 to 16

Answer:

220%

Step-by-step explanation:

Amount of change= Greater value- Lesser value

= 16-5

=11

Find the percent increase. Round to the nearest percent.

Percent change= Amount of change

                             Original Amount

=11/5

=2.2

=220%

Hope this helped  

Please help also please explain

Answers

Step-by-step explanation:

By AA, the two triangles in the figure are similar.

therefore, 10/15 = x/18

180 = 15x

x = 12

Topic: congruence and similarity

If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!

Tyler incorrectly says that the constant term of (x + 4)(x - 4) is zero.
a. What is the correct constant term?
b. What is Tyler's mistake? Explain your reasoning.

Answers

Answer:

a. -16 is the constant

b.if you expand the equation it would be x^2-16, and the constant is -16

Solving the expression (x + 4)(x - 4) ; the constant term in the expression is - 16 and not 0

To solve, we need to expand the expression : (x+4)(x-4)

Expanding the expression :

(x + 4)(x - 4)

Opening the bracket :

x² - 4x + 4x - 16

x² - 16

The constant term in the expression, is - 16 as it is the value without a variable.

Therefore, Tyler's mistake is incorrectly stating that the constant value is 0 instead of - 16

Learn more :https://brainly.com/question/18109354

The constants a, b, and c are positive. Solve the inequality for x.

ax-b is less than c

Answers

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[tex]ax - b < c[/tex]

Add sides b

[tex]ax - b + b < c + b[/tex]

Simplification

[tex]ax < b + c[/tex]

Divide sides by a

[tex] \frac{a}{a} x < \frac{b + c}{a} \\ [/tex]

[tex]x < \frac{b + c}{a} \\ [/tex]

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plz help its pass due

Answers

The third one

x,y —>-x,-y

Because 2,-1–>-2,1

Answer:

C

Step-by-step explanation:

The coordinates went from (4,1) to (-4,-1). This means it went from (x,y) to (-x,-y)

lg(5x+10)+2lg3=1+lg(4x+12)
need them fast with steps

Answers

Answer:

x=6

Step-by-step explanation:

log(5x+10)-log(4x+12)=1-2log(3)

log(5x+10/4x+12)=1-2log(3)

log(5x+10/4x+12)=log(10)+log(3^-2)

log(5x+10/4x+12)=log(10×3^-2)

log(5x+10/4x+12)=log(10×1/9)

log(5x+10/4x+12)=log(10/9)

5x+10/4x+12=10/9

9(5x+10)=(4x+12)10

45x+90=40x+120

5x=30

x=6

if you like my answer. Please mark me as brainliest

Square numbers between 300 and 400

Answers

324, 361, 400

18^2=324
19^2=361
20^2=400

1. Kites are on sale: 4 kites for $11. If Josh
spent $35.75 on kites during the sale, how
many kites did he buy? Write and solve a
proportion to answer.
C. 22 kites
A. 9 kites
B. 13 kites
D. 98 kites

Answers

Answer:

the kites are 4 for $11 then Josh buy x amount with $35.75 on kites. So  what you do is you didved each numder and the the one that is closest to that numder is the right answer so the answer is 13 kites

please help a polynomial of degree 4 has 3-2i and 1+i as zeros. Are there any x-intercepts? Explain why?​

Answers

Answer:

Answer:I can't read or see it

Step-by-step eAnswer:I can't read or see itxplanation:

Given h(x) = 4x – 5, solve for x when h(x) = 7.

Answers

Answer: x = 3 when  h(x) = 7.

Step-by-step explanation:

h(x) = 4x -5      To solve for x when h(x) = 7,  you will set the expression 4x -5 equals 7 to solve for x.

4x -5 = 7    Add 5 to both sides

   +5   +5

4x = 12       Divide both sides by 4.

x= 3

Is 4 a solution to the compound inequality “x > 0 ​AND​ x < 7”

Answers

Answer:

Yes

Step-by-step explanation:

4 is greater than 0, and 4 is less than 7

Answer:

yes

Step-by-step explanation:

x is greater than 0 and also less than 7 in this case.

(hi again furydrill! i just answered one of your questions a minute ago!)

What is the quotient?

Answers

Answer:

-0.4

I am pretty sure

Step-by-step explanation:

Ms sherman had 36 guests at her house for a party. Each guest brought 1 item
•One-third of the guests brought cupcakes
•one-half of the guests brought chips
•The rest brought drinks
How many guests brought drinks

Answers

Answer: 216?

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

one third of 36 is 12

one half of 36 is 18

and

12+18=30

36-30= 6

please help , what’s the value of x?

Answers

Answer:

x = 34

Step-by-step explanation:

[tex]x=34[/tex]

What is 0.74 + (-3/5)

Answers

The answer is 0.14!!!

Answer:

It equals 0.14

Step-by-step explanation:

16+x/13=18 What Is the Steps

Answers

Answer:

x=26

Step-by-step explanation:

Simplify both sides of the equation.

16+

x

13

=18

16+

1

13

x=18

1

13

x+16=18

Step 2: Subtract 16 from both sides.

1

13

x+16−16=18−16

1

13

x=2

Step 3: Multiply both sides by 13.

13*(

1

13

x)=(13)*(2)

x=26

Which of these equations correctly identify factors of 15? Check all that apply.

15 ÷ 1 = 15
15 ÷ 2 = 7
15 ÷ 3 = 5
15 ÷ 5 = 3
15 ÷ 10 = 5

Answers

Answer:

15÷1=15

15÷3=5

15÷5=3

Step-by-step explanation:

Answer:

15 divided by 1 = 15

15 divided by 3 = 5

15 divided by 5 = 3

Step-by-step explanation:

Find all the missing elements

Answers

Answer:

[tex] b = 5.5 [/tex]

[tex] c = 11.2 [/tex]

Step-by-step explanation:

Given:

A = 96°

B = 25°

C = 59°

a = 13

Required:

b and c

SOLUTION:

Use Sine Rule to find the measure of a and b, respectively.

✍️Thus, to find b, use,

[tex] \frac{a}{sin(A)} = \frac{b}{sin(B)} [/tex]

Plug in the values

[tex] \frac{13}{sin(96)} = \frac{b}{sin(25)} [/tex]

Multiply both sides by sin(25)

[tex] \frac{13}{sin(96)} \times sin(25) = \frac{b}{sin(25)} \times sin(25) [/tex]

[tex] \frac{13 \times sin(25)}{sin(96)} = b [/tex]

[tex] b = 5.5 [/tex] (nearest tenth)

✍️To find c, use,

[tex] \frac{a}{sin(A)} = \frac{c}{sin(C)} [/tex]

Plug in the values

[tex] \frac{13}{sin(96)} = \frac{c}{sin(59)} [/tex]

Multiply both sides by sin(59)

[tex] \frac{13}{sin(96)} \times sin(59) = \frac{c}{sin(25)} \times sin(59) [/tex]

[tex] \frac{13 \times sin(59)}{sin(96)} = c [/tex]

[tex] c = 11.2 [/tex] (nearest tenth)

- A rectangular pool has an area of 140 square feet. If the length of the
pool is 16 feet, what is its width?

Answers

Answer:

8.75 feet

Step-by-step explanation:

Use the area formula, A = lw, where l is the length and w is the width

Plug in the area and length, and solve for w:

A = lw

140 = 16w

8.75 = w

So, the width is 8.75 feet

Answer:

8.75 ft

Step-by-step explanation:

Use the area formula, A = lw, where l is the length and w is the width

Plug in the area and length, and solve for w:

A = lw

140 = 16w

8.75 = w

So, the width is 8.75 feet

Benito wants to buy a car. He is considering two different models. Model A is 6 7/8 feet wide. Model B is 75 inches wide. Express the width of each car using feet using a decimal. Which car is bigger?

Answers

Model A is the bigger car.

what is the decimal form for 3750?

Answers

Answer:

.3750

Step-by-step explanation:

sorry if this is wrong. I don't understand

Consider 8x2 - 48x = -104.

Answers

Answer:

2.5

Step-by-step explanation:

plz mark brainliest

Answer:

a=1: x2 + -6      x=-13

Step-by-step explanation:

Complete the square:

x2 – 6x + 9  =–13 + 9

Factor the trinomial and simplify:

(x + -3 )²= -4

Use the square root property of equality to solve

(x  – 3)2 = –4.

The solutions are

3 ± 2i

Help me pls thank you!!

Answers

C.

is the answer because it states that you can use three sixes in order to make 18
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