For quardatic equations of the form ax^2+bx+c = 0, we have
sum of roots = -b/a
products of root = c/a

minimum is achieved at x = -b/2a

1) b/a=-10
sum of roots = -b/a = 10 ... sufficient
2) minimum value of f(x) is attained at x=5
-b/2a = 5 => -b/a = 10 ----- Sufficient

Ans D

I could be wrong, but I find the question unsatisfactory in the sense that its solution lacks the sort of reasoning that is brought to bear on official questions. Simply stated, someone who knows the formulas related to the roots of a quadratic equation will simply regurgitate that information and answer comfortably without much thought at all. Someone who has not memorized such information will labor over the question or resort to guessing. (If you look at the related questions at the bottom of the page, none are official, and they involve this same sort of one-note line of reasoning to arrive at the answer.) Now, I am not saying that a knowledge of basic formulas and equations is not requisite to performing well on the exam. I doubt most people would be able to derive the equation to find the volume of a right circular cylinder, for example, and to solve a question based on that equation within roughly two minutes. However, my point is that in such official cylinder questions, while the volume equation serves as a foundational basis to engage with the problem, there might be some other point that requires a little thinking to answer the question (e.g., the liquid inside only partially fills the cylinder, or the cylinder is turned on a different side). This question does not look realistic to me for GMAT™ purposes.

For anyone interested in understanding why the sum of the roots of a quadratic is -b/2a, etc., feel free to check out this page from Cuemath. Good luck with your studies.

- Andrew
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