You can choose the same 3 answers for all of them two real solutions one real solution no real solutions

Let  be a quadratic equation; a is not equal to 0.

The discriminant of  is defined as .

The number of (real number) solutions of a quadratic equation is determined by the discriminant as follows:

If D>0, then the equation has 2 (different) solutions.

If D=0, the equation has 1 real solution.

If D<0, the equation has no real solutions.

Thus, we calculate the discriminants in each equation, and decide on the number of solutions accordingly:

i) a=-3, b=1, c=12;  D=(-3)^2-4*1*12=9-48<0 (no real solutions).

ii) a=2, b=-6, c=5; D=2^2-4*(-6)*5=4+120>0 (2 real solutions).

iii) a=1, b=7, c=-11;  D=1^2-4*7*(-11)=1+28*11>0 (2 real solutions).

iv) a=-1, b=-8, c=-12; D=(-1)^2-4(-8)(-12)=1-48*12<0 (no real solutions).

no solution, 2 solutions, 2 solutions, no solution.