Given f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3, determine whether or not x-a and x+a are factors of f(x). Hence, find, in terms of a, the roots of f(x) = 0.
thankyou so much

Answers

Answer 1

Answer:

Step-by-step explanation:

f(x) = 2x³ + ax² - 7a²x - 6a³

= 2x³ - 2a²x + ax² - a³ - 5a²x - 5a³

= 2x(x² - a²) + a(x² - a²) - 5a²(x+a)

= (2x+a)(x - a)(x + a) - 5a²(x + a)

= (x + a)[(2x + a)(x - a) - 5a²]

= (x + a)(2x² - ax - 6a²)

= (x + a)(2x + 3a)(x - 2a)

Answer 2

x-a is the factor of the equation and x + a is not a factor of the equation,

All the roots of the equation are x + a, 2x+3a, x-2a.

What is a cubic equation ?

"In algebra, a cubic equation in one variable is an equation of the form

ax^3+bx^2+cx+d=0

in which a is nonzero.

The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). "

Given equation is [tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3[/tex]

Now,

[tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3\\\\= 2x^3 - 2a^2x + ax^2 - a^3 - 5a^2x - 5a^3\\\\= 2x(x^2 - a^2) + a(x^2 - a^2) - 5a^2(x+a)\\\\= (2x+a)(x - a)(x + a) - 5a^2(x + a)\\\\= (x + a)[(2x + a)(x - a) - 5a^2]\\\\= (x + a)(2x^2 - ax - 6a^2)\\\\= (x + a)(2x + 3a)(x - 2a)[/tex]

Hence, the roots of the equation are x + a,  2x  +3a,  x - 2a.

To know more about cubic equation here

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Related Questions

There are 6 people in George's family. How much did George's mom pay for tickets? Show how you found your solution.

Answers

Answer:

$75

Step-by-step explanation:

To find out how much George's mom paid for the 6 tickets, first find the unit rate, that is cost per ticket.

The unit rate/constant of proportionality between cost of tickets (y) and number of tickets (x) can be calculated using the coordinates of any points on the graph.

Using (4, 50), this means that 4 tickets cost $50.

Unit rate/constant of proportionality = y/x = 50/4 = 12.5

This means a ticket costs $12.5.

Therefore, 6 tickets would cost:

6 tickets × $12.5 = $75.

George's mom paid $75 for the tickets?

Last question I think HELP ME ITS FIXING TO BE OVER DUE!!!

Answers

Answer:

I am not good at this but a good app for math is Math

way

~Hope this helps!!Stay safe~

Find the third, fifth, and tenth terms of the sequence described by the rule.
A(n)= -5+ (n - 1)(6)
A(3) =
(Simplify your answer.)
A(5) =
(Simplify your answer.)
A(10) =
(Simplify your answer.)

Answers

A(3)= 6
A(5)= -19
A(10)= -49

Solve for y.
4(y - 8) + 6 = 58

Answers

Answer:

[tex]4(y - 8) + 6 = 58 \\ or \: 4y - 32 + 6 = 58 \\ or \: 4y - 26 = 58 \\ or \: 4y = 58 + 26 \\ or \: 4y = 84 \\ or \: y = \frac{84}{4} \\ or \: y = 21[/tex]

21 is the answer.....

Hopes to get BRAINLIEST......Hopes it helps you.......

Thank you ☺️

Help me plzzzzzzzzzz​

Answers

Answer:

∠f=34°

Step-by-step explanation:

the answer for this is 34°

Rich and Betsy Cuik started a small business. They manufacture a microwavable coffee-to-go cup called Cuik Cuppa Coffee. It contains spring water and ground coffee beans in a tea-bag-like pouch. Each cup costs the company $1.00 to manufacture. The fixed costs for this product line are $1,500. Rich and Betsy have determined the demand function to be q = -1,000p + 8,500, where p is the price for each cup.
Write the expense equation in terms of the demand, q.
Express the expense equation found in part (a) in terms of the price, p.

Answers

Answer: E= 1.00q + 1,500

Step-by-step explanation:

Find the value of X in the triangle

Answers

Answer:

             44°

Step-by-step explanation:

[tex]m\angle BAC=180^o-124^o=56^o\\\\\overline{AB}=\overline{BC}\quad\implies\quad m\angle BCA=m\angle BAC=56^o\\\\m\angle ABC=180^o-2\cdot56^o=68^o[/tex]

[tex]m\angle DBE=m\angle ABC=68^o[/tex]   {vertical angles}

[tex]\overline{BD}=\overline{DE}\quad\implies\quad m\angle DEB=m\angle DBE=68^o\\\\m\angle x=180^o-2\cdot68^o=44^o[/tex]

What is the slope of the line that passes through the points (-6 , -4) and ( -12 , -4)? Write in simplest form plssss!

Answers

Answer:

the slope is zero

Step-by-step explanation:

Answer:

I think that: slope (m) = 0

Step-by-step explanation:

the equation of slope is m = y2-y1/x2-x1

so, y2 = -4, y1 = -4, and x2=-12, and x1= -6

Just substitute them into the equation:

m = -4 - -4 / -12- -16

m = 0

The slope is equal to 0

I hope this helps!

the table below represents a proportional relationship the unit rate of the relationship is ______?

Answers

Answer:

It is 3

Step-by-step explanation:

I know it is 3 because multiply every nimber on the and you will get the number frome the bottom.

What is the domain of the function in this table

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The main fuction is mulitiply by 2 each 1 point

Step-by-step explanation:

The scale of a map is 2/5 inches represents 3 miles. How much does 1 inch represent?

Answers

Answer:

DEEEEEEZ NUTTTTTTZ

Step-by-step explanation:

The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 50t - 2t2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop? (4 points)

Answers

Answer:

t=12.5s

Step-by-step explanation:

s(t) = 50t - 2t^2

v(t) = 50 - 4t

a(t) = -4

When v(t) = 0, the car stops.

v = u +at

0 = 50 + (-4)t

t = 12.5

The price of a DVD is $24.00 plus 8% sales tax.What is the sales tax on this DVD in dollars and cents?
A) 25
B) 0.8
C) 1.92
D) 30

Answers

Answer:

Your answer is C) 1.92

Hope this helps ^_^

Answer:

Sales tax is $1.92 or 192 cents.

Step-by-step explanation:

Given the price of a DVD is $24.00 plus 8% sales tax.

we have to find the sales tax on this DVD in dollars and cents.

The sales tax is 8% can be calculated as

8/100 X $24

1.92

In cents

as one dollar equals 100 cents

∴ 1.92 dollar = $1.92 = 192 cents

Hence, sales tax is $1.92 or 192 cents.

So your answer is C!!

pls help me, i’ll give brainliest

Answers

Answer:

the set of integers

Step-by-step explanation:

The width of a rectangle is its length. The perimeter of the rectangle is 300 ft. What is the length, in feet, of the rectangle?​

Answers

Answer:

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Width: 38 ft

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Step-by-step explanation:

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Answers

Answer:

I would have to go with B.) 129

Step-by-step explanation:

because 54+130+130+97 is 411 and 540-411 is 129

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Answers

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To get:

6, 12, 18, 24, 30,36

2, 3, 4, 5, 6- if that’s what you meant

equivalent ratio to 2:5

Answers

Answer:

4:10

8:20

16:40

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Step-by-step explanation:

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Answers

M= -2
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Dashed below

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Answers

Answer:

-3.5

Step-by-step explanation:

mark on the left side of the number line where -3.5 is.

PLEASE WILL GIVE BRAINLIEST!!

Answers

Step-by-step explanation:

Hey there!

According to the figure;

9v = 31° + 4v + 44° { The exterior angle is equal to the sum of opposite adjacent interior angles}

9v-4v = 44°+31°

5v = 75°

v = 75°/5

Therefore, v= 15°.

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Answers

Answer:

Step-by-step explanation:

TANGERINES

Answer:

of what ? finish the question

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Answers

Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

A fraction is in simplest form when no other factor but 1 will divide into the numerator/ denominator

[tex]\frac{5}{10}[/tex] ← divide numerator/ denominator by 5

=[tex]\frac{1}{2}[/tex]

[tex]\frac{4}{5}[/tex] ← is in simplest form

[tex]\frac{6}{10}[/tex] ← divide numerator/denominator by 2

= [tex]\frac{3}{5}[/tex]

[tex]\frac{8}{12}[/tex] ← divide numerator/denominator by 4

= [tex]\frac{2}{3}[/tex]

[tex]\frac{4}{5}[/tex] is the only fraction given in simplest form

PLEASE HELP ME I ONLY HAVE 10 MINS TO FINISH ALL MY ASSIMENTS, WILL GIVE BRAINLIEST AND 15 POINTS
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Step-by-step explanation:

Write the equation of a line with a slope of 5 and contains the point (-6, 2)

Answers

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

C x 20 + R x 20 or

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Answers

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Step-by-step explanation:

Answer:

The answers are:

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See attachment for math work and answer.

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