Final answer:
The correct solutions for the quadratic equation 3x^2 - 7x + 4 = 0 are x = 4/3 and x = 1. Option D would be close, but no given options match the calculated solutions exactly as D associates x = 1 with another incorrect value, x = 4, and not 4/3.
Step-by-step explanation:
The question asks us to solve the quadratic equation 3x² - 7x + 4 = 0. To find the values of x that satisfy this equation, we use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Here, a = 3, b = -7, and c = 4. Substituting these values into the formula, we determine:
x = (7 ± √((-7)² - 4(3)(4))) / (2(3))
x = (7 ± √(49 - 48)) / 6
x = (7 ± √(1)) / 6
Since √(1) equals 1, we have two possible solutions for x:
x = (7 + 1) / 6 = 8 / 6 = 4 / 3
x = (7 - 1) / 6 = 6 / 6 = 1
Thus, the solutions for x are x = 4/3 and x = 1. However, these solutions do not exactly match the options provided. The correct form of the solutions should convert the fraction 4/3 to its equivalent, which is x = 1 ⅓, none of the given options (A, B, C, D) is fully correct. In this case, the closest correct option based on the given solutions could be x = 1, which is included in options A, C, and D, but they all pair x = 1 with another incorrect value.