1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tanya [424]
3 years ago
6

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

Mathematics
1 answer:
scZoUnD [109]3 years ago
8 0

Answer:

c^2 = 9dp

Step-by-step explanation:

Given

dx^2 + cx + p = 0

Let the roots be \alpha and \beta

So:

\alpha = 2\beta

Required

Determine the relationship between d, c and p

dx^2 + cx + p = 0

Divide through by d

\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0

x^2 + \frac{c}{d}x + \frac{p}{d} = 0

A quadratic equation has the form:

x^2 - (\alpha + \beta)x + \alpha \beta = 0

So:

x^2 - (2\beta+ \beta)x + \beta*\beta = 0

x^2 - (3\beta)x + \beta^2 = 0

So, we have:

\frac{c}{d} = -3\beta -- (1)

and

\frac{p}{d} = \beta^2 -- (2)

Make \beta the subject in (1)

\frac{c}{d} = -3\beta

\beta = -\frac{c}{3d}

Substitute \beta = -\frac{c}{3d} in (2)

\frac{p}{d} = (-\frac{c}{3d})^2

\frac{p}{d} = \frac{c^2}{9d^2}

Multiply both sides by d

d * \frac{p}{d} = \frac{c^2}{9d^2}*d

p = \frac{c^2}{9d}

Cross Multiply

9dp = c^2

or

c^2 = 9dp

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

You might be interested in
What is 5/11 in decimal form? (round your answer to the nearest hundredth.)?
natita [175]
5/11 in decimal form is .45
4 0
3 years ago
Help please 15 points
Margaret [11]

it took to long for you to rkgnhyh2gnb 45kljhnt4kjl ht3kltnhkj3rgn4tn2t4kb ktnhkjthk6l

7 0
3 years ago
I REALLY NEED HELP PLEASE
Nezavi [6.7K]

Answer:

10

Step-by-step explanation:

given

\frac{s + ( - 7)}{ - 1}

we first need to simplify the expression before we find it's value when s=-3

positive times negative=negative

so the equation becomes

\frac{s - 7}{ - 1}

substituting s=-3 into the equation.

\frac{ - 3 - 7}{ - 1}

=

\frac{ - 10}{ - 1}

=the negatives cancel out leaving

= 10

7 0
3 years ago
Three dentists wanted to compare the ages of their patients. They each calculated their patients’ mean age and the mean absolute
Alexus [3.1K]
Dr. Appiah’s patients’ ages vary less than do Dr. Singh’s patients’ ages.


GARBAGE DAY!
3 0
3 years ago
Read 2 more answers
What are the coefficients for the binomial expansion of (p+q)^6
seropon [69]

Answer:

1 6 15 20 15 6 1

Step-by-step explanation:

To figure this out, we need to look at Pascal's Triangle, which is a tricky little way to find the coefficients for any binomial expression like this! Check the attached photo.

Because this is to the sixth, we need the 6th row, which is <u>1 6 15 20 15 6 1.</u> From this, we know that those numbers are the coefficients!

8 0
3 years ago
Read 2 more answers
Other questions:
  • Graph the line that contains the point (o,3) and has a slope of 1/2
    15·1 answer
  • Standard algorithm 3÷5316
    13·1 answer
  • Can I Get Help With This:​
    10·1 answer
  • You have 20 shirts in your closet 4 blue 7 red 3 green and 6 black you pick one without looking what is the probability that you
    15·1 answer
  • A deep sea driver descended from a rock with an elevation of -45.5 feet to a coral reef with an elevation of -88.5 feet. How far
    9·1 answer
  • Maria invests $8,000 in a bank account, which pays 9% annual interest, compounded yearly. What will be Maria’s account balance a
    10·1 answer
  • Solve for x:
    10·1 answer
  • 2m^2-5m-3=0 by factorization​
    7·1 answer
  • If x=-1 , y=1 and z =2 then find the value of. a . 2x+3y +4z b. 5x2 +3y2+7z2​
    6·1 answer
  • A circle has a radius of 8cm. What is the AREA? Use this formula - A = pi X radius squared.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!