The roots of a quadratic equation ax²+bx+c=0 can be determined by calculating the discriminant Δ=b²-4ac.
If Δ>0, there are two distinct real solutions.
If Δ=0, there is one real solution.
If Δ<0, there are no real solutions and two complex solutions.
\(3x^2+12x-3=0 \\ \\
a=3 \\ b=12 \\ c=-3 \\ \\
\Delta=b^2-4ac=12^2-4 \times 3 \times (-3)=144+36=180\)
Δ>0, so there are two distinct real solutions. The answer is A.
