Absolute Value Equation

[nycmathguy]

Set 1.2
Question 64
David Cohen

Explain why there are no real numbers that satisfy the equation | x^2 + 4x | = -12.

 

[MathLover1]

here are reasons why certain absolute value functions do not have real solutions

 

[nycmathguy]

here are reasons why certain absolute value functions do not have real solutions

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?

 

[MathLover1]

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

 

[nycmathguy]

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

What do you mean by magnitude? When I think of magnitude, I think of vectors.

 

[MathLover1]

that is same meaning, the magnitude of a vector is a number, or a scalar, or a numerical value

 

[nycmathguy]

that is same meaning, the magnitude of a vector is a number, or a scalar, or a numerical value

Ok. Check out my post Cubic Equations.