Step-by-step explanation
Since we have the function:
![f(x)=3x^2+12x-5](https://img.qammunity.org/2023/formulas/mathematics/college/2vxy3owimmtx4yk9g6d3lzt5lsm2k4wkpy.png)
The discriminant of the quadratic is given by the following expression:
![b^2-4ac](https://img.qammunity.org/2023/formulas/mathematics/high-school/ovf2g76yckt0a2siciwy3cau25hp7z886x.png)
Where a=3, b=12 and c=-5:
Plugging in the terms into the expression:
![12^2-4*3*(-5)](https://img.qammunity.org/2023/formulas/mathematics/college/v0w0ymmutocdbrbyqxuen8wvriz78i9vii.png)
Multiplying terms:
![144+60](https://img.qammunity.org/2023/formulas/mathematics/college/w5dxhe42fp2x99k6x5h7pvnk3uj4lwqjda.png)
Adding numbers:
![Discriminant=204](https://img.qammunity.org/2023/formulas/mathematics/college/v3pk8phlw3i840hgpyjt1royfcasjeji1u.png)
In conclusion, since the discriminant is >0 , the appropriate option is OPTION A.