EXPLANATION
Since we have the function:
[tex]f(x)=3x^2+12x-5[/tex]
The discriminant of the quadratic is given by the following expression:
[tex]b^2-4ac[/tex]
Where a=3, b=12 and c=-5:
Plugging in the terms into the expression:
[tex]12^2-4*3*(-5)[/tex]
Multiplying terms:
[tex]144+60[/tex]
Adding numbers:
[tex]Discriminant=204[/tex]
In conclusion, since the discriminant is >0 , the appropriate option is OPTION A.
