One of the roots of the quadratic equation dx^2+cx+p=0 is twice the other, find the relationship between d, c and p

Answers

Answer 1

Answer:

[tex]c^2 = 9dp[/tex]

Step-by-step explanation:

Given

[tex]dx^2 + cx + p = 0[/tex]

Let the roots be [tex]\alpha[/tex] and [tex]\beta[/tex]

So:

[tex]\alpha = 2\beta[/tex]

Required

Determine the relationship between d, c and p

[tex]dx^2 + cx + p = 0[/tex]

Divide through by d

[tex]\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0[/tex]

[tex]x^2 + \frac{c}{d}x + \frac{p}{d} = 0[/tex]

A quadratic equation has the form:

[tex]x^2 - (\alpha + \beta)x + \alpha \beta = 0[/tex]

So:

[tex]x^2 - (2\beta+ \beta)x + \beta*\beta = 0[/tex]

[tex]x^2 - (3\beta)x + \beta^2 = 0[/tex]

So, we have:

[tex]\frac{c}{d} = -3\beta[/tex] -- (1)

and

[tex]\frac{p}{d} = \beta^2[/tex] -- (2)

Make [tex]\beta[/tex] the subject in (1)

[tex]\frac{c}{d} = -3\beta[/tex]

[tex]\beta = -\frac{c}{3d}[/tex]

Substitute [tex]\beta = -\frac{c}{3d}[/tex] in (2)

[tex]\frac{p}{d} = (-\frac{c}{3d})^2[/tex]

[tex]\frac{p}{d} = \frac{c^2}{9d^2}[/tex]

Multiply both sides by d

[tex]d * \frac{p}{d} = \frac{c^2}{9d^2}*d[/tex]

[tex]p = \frac{c^2}{9d}[/tex]

Cross Multiply

[tex]9dp = c^2[/tex]

or

[tex]c^2 = 9dp[/tex]

Hence, the relationship between d, c and p is: [tex]c^2 = 9dp[/tex]


Related Questions

PLEASE HELP ASAP!!! WILL MARK BRAINLIEST!!! (Solving Equations with Distributive Property)

1) -1/2(12p-42) = -33


2) -3 + 2/3(6n-42) = -51

Answers

Step-by-step explanation:

Answer and explanations are in the pic

please help
me solve this

Answers

Answer:

A

Step-by-step explanation:

I literally just did the test a week ago and gt the answer correct

The coordinates
(

2
,

3
)
(−2,−3) lie on line
r
r. Which equation could represent line
r
r?

Answers

Answer:

A y = -12x – 21 By = -2x – 7 O y = 5x – 7 D y = -2x – 1

Step-by-step explanation:

HOPE THIS HELPS !! <3

Nancy bought a package of 4 spiral notebooks for a total cost of $18.25. Which equation represents p, the cost, in dollars, of each notebook?

Answers

Answer:

p=18.25/4

p=$4.56 (when you round)

Step-by-step explanation:

Brainliest?!?!?!?!?

Karem drives his car and 96 miles in 1 1/2 hours of karem continues to drive at this rate how many miles will you travel in 2 1/2 hours?

Answers

Answer:you have to find how much hrs are together the multiply by 2 and dived really i just need points

Step-by-step explanation:

Mr. Garcia's yard is 22 feet by 31 feet. If he wanted to put a fence around this yard, how many feet of fence would he need?

Answers

Answer:

53

Step-by-step explanation:

The Students' Conjectures: You and Uyen are writing a grant proposal for $50,000 to
provide wireless Internet access to a rural community in South Korea. Complete the
table to summarize Uyen's idea about the percentage of the population that can get
Internet access for $50,000. (1 point)
Classmate
Conjecture
Uyen

Answers

100,000 beacause of the internet x 2

1/3 + (3x+12) = 6x -11

Answers

Answer:

x = 70/9

Step-by-step explanation:

Answer:

70/9

Step-by-step explanation:

write the equation for the inverse of the function y=pi/4+sinx

Answers

Answer:

Step-by-step explanation:

Sine doesn't have an inverse, until you restrict the domain to -pi/2 to pi/2. If you don't restrict the domain, then the inverse doesn't exist. Im going to assume the domain is restricted.

Switch the x and y values

[tex]x= \pi/4+ \sin(y)[/tex]

Subtract pi/4 on both sides

[tex]x- \pi/4= \sin(y)[/tex]

Take the arcsine of both sides

[tex]\arcsin(x- \pi/4)=y[/tex]

Answer:

C.

Step-by-step explanation:

correct on edg

graph the inequality

Answers

Answer:

D

Step-by-step explanation:

jqiwisksjsnsnjowowklqk

the answer is D

sjdjdikckckskdkvkocdfoc

Red balloons is 15 blue balloons is 10 what is the ratio of red to blue

Answers

Answer:

3:2

Step-by-step explanation:

15 to 5 in simplest form you caan multiply by 5 so in simplest form its

5x3=15

5x2=10

so anwswer is 3:2

plz mark brinliest

15 to 10 because since there is 15 red balloons and 10 blue balloons so 15 to 10 you can write it in multiple like 15:10

Simplify 3xy - 9xy + 11y

Answers

-6xy+11y
Shehshdhdhsbsvsvsvsvs

-y · (6x-11)

Hope that helps

pls help me with this problem its due in 10 minutes i do not need a full explanation

Answers

Answer:

20,781.64[tex]in^{3}[/tex]

Step-by-step explanation:

V = [tex]3.14*21^{2} *\frac{43}{3}[/tex]

good luck, i hope this helps :)

Given Angle 1 = Angle 2, find X.



X =

Answers

Answer:x=6

Step-by-step explanation:

100 POINTS PLEASE HELP ASAP!!!!!!!!!!!

Answers

Answer:

its the first one

Step-by-step explanation:

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⣿⣿⣿⣿⠟⠩⠶⣾⣿⡿⢯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠏⠀⠀⠈⠉⠀⣠⢤⠈⠋⠀⢠⣄⠉⢻⣿⣿⣿⣿⠃⠈⢿⣿⣿⣿⣿⣿

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⡏⠀⠀⠠⣤⠦⣭⣙⣛⠛⠋⠁⠀⠙⠛⢉⣻⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠈⣿

⡇⠀⠀⠀⠛⠮⣽⣒⣻⣭⢽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿

⡟⠳⢤⣤⣀⣀⣀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣴⣾⣿

⣇⠀⠀⠀⠀⠉⠉⠈⠁⠈⠉⠉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⣶⠿⠿⣷⡄⠈⣠⣶⠿⢿⣶⡄⠉⣡⣶⠿⠿⣶⡄⠄⣿⡇⢀⣾⡿⠃

⣿⣏⠄⠄⠄⠄⢰⣿⡇⢀⠄⣿⣿⠄⣿⡏⠄⠄⠄⠄⠄⣿⣿⣿⣿⡀

⠹⣿⣄⣠⣶⡆⠄⢿⣷⣀⣠⣿⡟⠄⢻⣷⣄⣠⣶⠆⠄⣿⡏⠈⢿

yall like that ;)?

A rectangle has a width of 2x and a length of 2x+5, what is the area?

Answers

Answer:

what ever the next person says

Step-by-step explanation:

please help me with this question fast!!!!

Answers

reflection and translation

PLEASE HELP!!!! WILL GIVE BRAINLIEST!!!!!! <3

Answers

Answer: The numbers go from left to right on the table in this order: 0, 3, 4, 3, 0, -5.

To do the problem, you put the x - value in place of where the x is in the equation above (y = 4 - x^2) and then you put what y equals in the box after you finish.

Good luck, hope this helped!!

write the sentence as an equation, 341 is the same as 19 divided by b

Answers

Answer:

19/b =341

Step-by-step explanation:

Division in algebra is shown in fractions so if you put 19 over b it means 19 divided by b.

19/b=341 the dash is meant to be the division sign

Raul’s sister is 6 years older than he is. What is Raul’s age if Raul’s sister is 19 years old? r=?

Answers

Answer:

13

Step-by-step explanation:

19-6

Answer:

Raul is 13 years old

Step-by-step explanation:

Algebra edg plz help!

Answers

Answer:

12

Step-by-step explanation:

Least common multiple of the numbers 2, 3, and 4 is 12

Answer:

3

Step-by-step explanation:

For them to at least be a whole number, it’s 3

I am giving brainliest to the right answer!

Answers

ok answer this, 7x150+10 and that should be your answer.

Answer:

x=20

Step-by-step explanation:

 there are two intersecting lines with two pairs of opposite angles each of the pairs are called vertical angles and if two angles are vertical, they are congruent

we know the angles are congruent, we also know (150=7x+10) and in order to solve for x we have to isolate x by subtracting 10 to both sides giving us  (140=7x )

divide by seven on both sides to isolate x and that will give you x=20.

hope this helps :) have a nice day !!

please help me !!!!!​

Answers

Answer:

61 feet

Step-by-step explanation:

We can use the pythagorean theorem to solve this answer (a^2 + b ^2 = c^2, c= longest length)

50^2 + 35^2 = 61.03.

Rounded to the nearest whole number, the answer is D.

Answer:

C

Step-by-step explanation:

It's a right triangle so you can use a squared +b squared =c squared

a and b are the legs of the triangle which in this case are 50 and 25 feet.

Plug them into the equation:

50^2+25^2=c^2

50 squared = 2,500

25 squared = 625

2,500 + 625= 3,125

so c squared is 3,125. To get c you need the square root which is ~55 feet

Find Sin D and sin E! Write the answer as a fraction and as a decimal. Round to four decimal places, if necessary! Please help me!

Answers

Answer:

sine D = 0.9459

sine E = 0.3243

Step-by-step explanation:

Mathematically, sine is the ratio of the opposite to the hypotenuse

The hypotenuse is the longest side and we have it as 37 in the diagram given

the opposite to angle E is 12

So the sine of E = 12/37 = 0.3243

For D , its opposite is 35

The sine of D = 35/37

sine of D = 0.9459

The triangle has an area of 7 7/8 cm2 and a base of 5 1/4 cm. What is the height?

Answers

the height is 2.8, I’m not really good at showing my work on this app

Answer:

3

Step-by-step explanation:

7 7/8÷51/4

3/2÷1/2

3

A=bh1/2

A=5 1/4×3×1/2

A=15 3/4×1/2

A= 7 7/8

(Mark as brainliest please)

You have 40 minutes to exercise at the gym, and you want to burn 300 calories total using both
machines. The amount of calories burned on each machine is shown in the picture below. How
much time should you spend on each machine?


Machine a burns 8 calories per minute machine b burns 6 calories per minute.

Answers

a and b are the minutes spent on machine A and machine B, respectively.

a+b = 40
b = 40-a

8a + 6b = 300
8a + 6(40-a) = 300
8a + 240 - 6a = 300
2a = 60
a = 30
b = 40-a = 10

30 minutes on machine A and 10 minutes on machine B

Factor using the GCF: 6x + 15

Answers

Answer:

3(2x + 5)

Step-by-step explanation:

What numbers go into both 6 and 15? What number is the largest of those numbers? The answer to both questions is 3, therefore we factor out the 3 using the distributive property

Answer:

It is 3(2x+5)

Step-by-step explanation:

Hope you get it right

The weather report says there is a 91% chance it will rain tomorrow. Should you get ready to use an umbrella?

Question 1 options:
1 Yes
2 No
3 maybe

Answers

yes
Even if it was 80%, you would still want to bring an umbrella just in case
Maybe. This is because even though it says 91%, the weather changes because of global warming which concludes to there not actually being any exact results but, still take an umbrella just to make sure.

Hope this answer was reasonable for you :)

What is the value of s?
units

Answers

The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the cesium frequency ΔνCs, the unperturbed ground-state hyperfine transition frequency of the cesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s-1.

which best describes two figures that are similar?​

Answers

Answer:

B

Step-by-step explanation:

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