Evaluate the Discriminant for the Equation $4 x ^ { 2 } + 12 x + 9 = 0$

question 356

Multiple Choice

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex.
- $4 x ^ { 2 } + 12 x + 9 = 0$

• A) Two distinct nonreal complex solutions
• B) Two distinct rational solutions
• C) One rational solution (a double solution)
• D) Two distinct irrational solutions

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Definitions:

Ear Canal

The tube that runs from the outer ear to the eardrum, transporting sound waves to the eardrum.

Sensorineural Hearing Loss

Hearing loss that occurs when neural structures associated with the ear are damaged. Neural structures include hearing receptors and the auditory nerve.

Conductive Hearing Loss

A type of hearing loss that occurs when sound waves cannot be conducted through the ear. Most types are temporary.

Tuning Fork

A tool made of metal with two prongs, used primarily to produce a specific tone or pitch for tuning musical instruments, as well as for auditory testing and in healing practices.