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
Julli [10]
3 years ago
5

Find an m > 0 such that the the equation x^4−(3m+2)x^2+m^2=0 has four real solutions that form an arithmetic sequence.

Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
4 0

Answer:

The value of m is 6.

Step-by-step explanation:

Here, the given equation,

x^4-(3m+2)x^2+m^2=0

x^4+0x^3-(3m+2)x^2+0x+m^2=0

Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )

Thus, we can write,

a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}

=\frac{0}{1}=0

\implies a=0----(1)

(-3b)(-b)+(-b)(b)+(b)(3b)+(3b)(-3b)+(-b)(3b)+(-3b)(b)=\frac{\text{coefficient of }x^2}{\text{coefficient of }x^4}}

=\frac{-3m-2}{1}

3b^2-b^2+3b^2-9b^2-3b^2-3b^2=-3m-2

-10b^2=-3m-2

\implies b^2=\frac{3m+2}{10}-----(2)

(-3b)(-b)(b)(3b)=\frac{\text{Constant term}}{\text{coefficient of}x^4}= m^2

9b^4=m^2

9(\frac{3m+2}{10})^2=m^2

9(\frac{9m^2+4+12m}{100})=m^2

81m^2+36+108m=100m^2

-19m^2+108m+36=0

19m^2-108m-36=0

19m^2-114m+6m-36=0

19m(m-6)+6(m-6)=0

(19m+6)(m-6)=0

\implies m=-\frac{6}{19}\text{ or }m=6

But m > 0,

Hence, the value of m is 6.

You might be interested in
how much material was used in the manufacture of 24000 celluloid dice,if each dice has an edge 1/4 inches?
Dovator [93]
<span>The volume of each celluloid die is (.25 x .25 x .25) = 0.015625 cubic inch.

To manufacture 24,000 of them, you need to start with <u>at least</u>

(24,000) x (0.015625) = <u>375 cubic inches</u>.

I don't know how celluloid is sold, so you should also keep in mind that
375 cubic inches = about 207.8 fluid ounces, or about 6.5 quarts.

I'm sure a bit more than that was used in the manufacture, since
there's always some wasted, spilled, or trimmed off of the edges. </span>
4 0
3 years ago
A cube has a side length of 6 cm. What is the volume of the cube, in cubic centimeters ​
Lady_Fox [76]

Answer:

V=216cm³

Step-by-step explanation:

V=216cm³

3 0
2 years ago
(3,-4, slope = undefined
Anni [7]



lines with undefined slope are vertical

equation are  in form of x constant

through the points ( 3 , -4)

the line is x=3


4 0
3 years ago
PLEASEEEEEE HELP GUYS!!!!!
alexira [117]
The answer is 1.2m/s/s
3 0
3 years ago
what is the probability of drawing two yellow marbles if the firat one is not placed back into the bag before the second draw
Step2247 [10]
It depends on the total number of marbles in the bag and the number of yellow marbles in the bag
4 0
3 years ago
Other questions:
  • Evaluate f(x) = sqrt(5x + 4) for x = 12
    6·1 answer
  • 10 less than a number translate this expression
    10·1 answer
  • Question: 1) Hi how are you?
    12·1 answer
  • If f(x)=2x^2+3x-4, find 2f(x)
    9·1 answer
  • Need help on answering number 9.
    8·2 answers
  • Can you please help me??
    14·1 answer
  • Drag each equation to show if it could be a correct first step to solving the equation 3(6+x)=24
    8·2 answers
  • You and your friends order food from a menu where each item costs the same amount. Write an expression in the simplest form that
    5·1 answer
  • What is the mass of 64 mL of a liquid with a<br> density of 2.7 g/mL?
    15·1 answer
  • The set of negative numbers are closed under division true or false if false explain
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!