IKMC 2027 - Grades 11-12 - Self-study SET 3 - Thematic Batch 3 Question 5

Question 5

Let M be positive and f (x)=πx²−Mx+π for real x. Suppose there exists a real a satisfying f (x)≤0. Which assertion below is certainly true?

Question illustration

M ≥ 3 π
f (x) ≤ 0 for every real x
There exists x with f (x) $\lt$ 0
f (1) ≤ 0
f (2) ≤ 0