Final answer:
To find c in the quadratic expression with the discriminant of -76, we use the discriminant formula D = b² - 4ac. Solving, c is found to be 55. None of the given options match this value, indicating a possible error in the question.
Step-by-step explanation:
To find the value of c in the quadratic expression 12x + c with a discriminant of -76, we will use the formula for the discriminant of a quadratic equation, which is D = b² - 4ac, where a, b, and c are coefficients in the quadratic equation ax² + bx + c = 0. Here, the coefficient a equals 1 (since the x² term is not preceded by any number, we assume it to be 1), and the coefficient b is 12.
Using the given discriminant value:
- D = b² - 4ac
- -76 = 12² - 4(1)c
- -76 = 144 - 4c
- -76 - 144 = -4c
- -220 = -4c
- c = 220 / 4
- c = 55
However, none of the provided options match the calculated value of 55. Therefore, there seems to be an error in the provided options or the discriminant given in the question.