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

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:

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

- 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

Which inequality represents the range of the relation graphed below?

Answers

Answer: I think it’s d

Step-by-step explanation:

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:

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❤❤

please help , what’s the value of x?

Answers

Answer:

x = 34

Step-by-step explanation:

[tex]x=34[/tex]

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

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.

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!

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

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

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)

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

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

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.

Square numbers between 300 and 400

Answers

324, 361, 400

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

What is 0.74 + (-3/5)

Answers

The answer is 0.14!!!

Answer:

It equals 0.14

Step-by-step explanation:

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

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 =)

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

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)

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

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]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

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

what is the decimal form for 3750?

Answers

Answer:

.3750

Step-by-step explanation:

sorry if this is wrong. I don't understand

Help me pls thank you!!

Answers

C.

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

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 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  

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