Final answer:
Using the quadratic formula on the equation b² - 52b + 96 = 0 yields two solutions: b = 50 and b = 2, which do not match any of the provided answer options. There may be a mistake in the equation or the answer choices that needs to be addressed.
Step-by-step explanation:
To find the value of b in the quadratic equation b² - 52b + 96 = 0, we use the quadratic formula: -b ± √b² - 4ac / (2a). In this case, our equation is already in the form ax² + bx + c = 0, where a = 1, b = -52, and c = 96. Applying these values to the quadratic formula, we have:
- b = (-(-52) ± √((-52)² - 4(1)(96))) / (2(1))
- b = (52 ± √(2704 - 384)) / 2
- b = (52 ± √2320) / 2
- b = (52 ± 48) / 2
This yields two possible solutions for b which are:
- b = (52 + 48) / 2 = 100 / 2 = 50 (not one of the provided options)
- b = (52 - 48) / 2 = 4 / 2 = 2 (not one of the provided options)
It seems there might be a mistake since neither of the solutions match the provided options. Please double-check the original equation or the provided answer choices.