IKMC 2027 - Grades 11-12 - Self-study SET 3 - Thematic Batch 3 Question 13

Question 13

The graph of f (x)=x²+px+q meets the two coordinate axes at three distinct points. The circle through those points meets the graph at a fourth point. What are that point’s coordinates?

Question illustration

(0, −q)
(p, q)
(−q/p, q²/p²)
(−p, q)
(1, p + q + 1)