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
Makovka662 [10]
3 years ago
5

^{2} x ^{2} + 2mx - 5 = 0" alt="3m ^{2} x ^{2} + 2mx - 5 = 0" align="absmiddle" class="latex-formula">

Answer?
With detailed steps please. Thank you! ​
Mathematics
1 answer:
crimeas [40]3 years ago
8 0

We could factor the usual way but let's try Dr. Po Shen Loh's "new" method.

3m^2x^2 + 2mx - 5 = 0

First step is to rewrite as a monic,

x^2 + \dfrac{2m}{3m^2} x - \dfrac{5}{3m^2} = 0

x^2 + \dfrac{2}{3m} x - \dfrac{5}{3m^2} = 0

Now we need two numbers which add to 2/3m and multiply to -5/3m².  If they add to 2/3m they average to 1/3m so they're 1/3m-u and 1/3m+u for some u.  The product of those two is -5/3m² so we write:

\left( \dfrac{1}{3m}-u \right)\left( \dfrac{1}{3m} +u \right) = -\dfrac{5}{3m^2}

\dfrac{1}{9m^2}-u^2 = -\dfrac{5}{3m^2}

u^2 = \dfrac{1}{9m^2} +\dfrac{5(3)}{(3)3m^2} = \dfrac{16}{9m^2}

u = \pm \dfrac{4}{3m}

So our equation

0=x^2 + \dfrac{2m}{3m^2} x - \dfrac{5}{3m^2}

factors as

0= \left( x +\dfrac{1}{3m}-\dfrac{4}{3m}\right) \left( x + \dfrac{1}{3m} + \dfrac{4}{3m}\right)

0= \left(x - \dfrac{1}{m}\right) \left(x +\dfrac{5}{3m} \right)

so has roots

x= \dfrac{1}{m} \textrm{ or } x = -\dfrac{5}{3m}

The more standard factorization with the same result is

0=(mx-1)(3mx+5)

You might be interested in
The Smith family is shopping for a new car and they are basing their decision on color and style. Explain how many color choices
Yanka [14]
Sample response: The Smith family has 2 choices to make, color and style. By the fundamental counting principle, the product of the number of choices of color and style must equal 8. So, there could be 1 color and 8 style choices, 2 colors and 4 styles, 4 colors and 2 styles, or 8 colors and 1 style.
3 0
3 years ago
Read 2 more answers
10 less than the product of 8 and 5
Nastasia [14]
The answer is 30.

8 x 5 =40

40 - 10 = 30
3 0
3 years ago
Read 2 more answers
For the function of F defined by f (x) = x + 8. what is the value of x when f (x) = 10
melomori [17]

Answer:

x = 2

Step-by-step explanation:

f(x) = x + 8

f(x) = 10

10 = x + 8

minus 8 from the both sides

10 - 8 = x

2 = x

x = 2

7 0
3 years ago
What is the difference in place value between 2 in 324 and the 2 in 0.324
icang [17]

Answer: the decimal should still be there but you don’t want to have a zero so 3.42 would be correcr

Step-by-step explanation:

4 0
3 years ago
In a certain town 215 boys and 265 girls were born last year. What is the probability that a child chosen at random from among t
Tanya [424]

Answer:

What I think it is from 5 through 25 or something like that

5 0
3 years ago
Other questions:
  • How would you determine whether time series regression or exponential smoothing is better?
    14·1 answer
  • Miguel is making an obstacle course for field day. At the end every sixth of the course,there is a tire. at the end of every thi
    9·2 answers
  • - If you divide a number by four and then add six, you<br> get eighteen. What is the number?
    6·2 answers
  • Plz help me :,( also show the work too /:
    7·1 answer
  • Will mark brainliest.
    12·1 answer
  • NEED HELP <br> what is the range?<br> |80 - 5x| = 4
    15·1 answer
  • Need help will mark brainliest
    7·2 answers
  • Why are inverse relationships between operations used to solve two step inequalities?
    8·1 answer
  • 3 to the second power x 3 x 3 x 3= <br><br> Simplified into exponential form
    6·2 answers
  • Simplify x+4 -5x-2?<br> plz i am dying help me
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!