Int. Alg.: find values making (2q + 8)/(q^2 + 4) undefined

[Helen]

I would appreciate someone helping me with this. I need to find all values that make the expression undefined:

2q + 8
--------
q^2 + 4

This is what I did.

q^2 + 4 = (q + 2)(q-2) = 0

q + 2 = 0 or q - 2 = 0

q = 2 or q = -2

Both 2 and -2 make the expression undefined. I don't think that 2 can be a replacement for q. The domain of f includes all real numbers except 2.

Am I figuring this right?

 

[Deleted member 4993]

Re: Intermediate Algebra

I need to find all values that make the expression undefined.

2q + 8
--------
q^2 + 4

This is what I did.

q^2 + 4 = (q + 2)(q-2) = 0 <---Incorrect

- to factorize like that you would need a negative (-) sign - that is - the expression should be q^2 - 4; you have q^2 + 4

 

[jwpaine]

\(\displaystyle \L \frac{2q + 8}{q^2 + 4}\)

Undefined at the zeros of the denominator, BUT no real values exist. (There is no real number such when squared equals a negative value) You can, however, say that \(\displaystyle \L \frac{2q + 8}{q^2 + 4}\) is undefined for \(\displaystyle \L q =\) +/- \(\displaystyle \L 2i\)

because \(\displaystyle \L (2i)^2 + 4 = 0\),

\(\displaystyle \L i\cdot i = -1\)

John

 

[Helen]

Intermediate Algebra

Thank you Subhotosh Khan and jwpaine for your help. Does both 2 and -2 make the expression undefined? Helen

 

[stapel]

Does both 2 and -2 make the expression undefined?

Do they make the denominator equal to zero? (Hint: Re-read the explanations provided earlier!)

Eliz.

 

[Helen]

Intermediate Algebra

Thank you, Eliz. Stapel. Appreciated! Helen