Final answer:
c) 8.The correct answer using the given lengths and quadratic formula is x = 3, which does not match any of the provided options. There might be an error in the question or the options presented.
Step-by-step explanation:
The correct answer is option c) 8. Since points A, B, and C are collinear, with B between A and C, the lengths AB, BC, and AC are connected by the equation AB + BC = AC. Plugging in the known lengths gives us the equation 3 + 5x = 2x². This is a quadratic equation and can be written as 2x² - 5x - 3 = 0.
To find the value of x, we use the quadratic formula x = (-b ± √(b²-4ac))/(2a), where a = 2, b = -5, and c = -3. Using these values we get the possible solutions for x.
By solving the quadratic equation, we find that x equals 3 and -0.5. However, since a length cannot be negative, we discard -0.5, and the answer is 3, which does not match any of the provided options. It seems there might be a mistake in the initially provided information or in the options given.
Based on the typical method of solving this problem, option c) 8 would not be the correct choice; it appears there might be an error in the question or the options provided as none match the solution 3.