Absolute Value Equation

Discussion in 'Other Pre-University Math' started by nycmathguy, Jul 12, 2021.

  1. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Set 1.2
    Question 64
    David Cohen

    Explain why there are no real numbers that satisfy the equation | x^2 + 4x | = -12.
     
    nycmathguy, Jul 12, 2021
    #1
  2. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    here are reasons why certain absolute value functions do not have real solutions
     

    Attached Files:

    MathLover1, Jul 12, 2021
    #2
    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    I understand the reasons stated. My question is why?

    Absolute value equations have no real solution when the graph does not touch or cross the x-axis and/or when the equation is equated to a negative number.
    Why? Do you know the why part of the answer?
     
    nycmathguy, Jul 12, 2021
    #3
  4. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    why?
    | x^2 + 4x | will be positive no matter what is the value of x
    absolute value is the magnitude of a real number without regard to its sign

    example:
    |12|=12 or |-12|=12 ->absolute value is is always positive, it just tells you a numerical value or measurement

    therefore | x^2 + 4x | =-12 =>a numerical value or measurement must be 12
     
    MathLover1, Jul 12, 2021
    #4
    nycmathguy likes this.
  5. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    What do you mean by magnitude? When I think of magnitude, I think of vectors.
     
    nycmathguy, Jul 13, 2021
    #5
  6. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    that is same meaning, the magnitude of a vector is a number, or a scalar, or a numerical value
     
    MathLover1, Jul 13, 2021
    #6
    nycmathguy likes this.
  7. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Ok. Check out my post Cubic Equations.
     
    nycmathguy, Jul 13, 2021
    #7
Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.
Similar Threads
There are no similar threads yet.
Loading...