Find the values of a for which the equation ax² + 11 x 3 = 0 has one root.

If the discriminant of a quadratic equation is less than 0, then the equation has no solutions, if the discriminant is 0, then the equation has exactly one solution, but if the discriminant is greater than 0, then there are two solutions.
So that the equation ax² + 11x – 3 = 0 has one root, the discriminant must be equal to 0.
Discriminant:
D = b ^ 2 – 4ac;
D = 11 ^ 2 – 4a * (- 3) = 121 + 12a.
Let us equate the discriminant to zero and find at what value of a this equality holds:
121 + 12a = 0;
12a = -121;
a = -121/12.
Answer: a = -121/12.