Latest Maths Olympiad Aptitude Question SOLUTION: Find all real values of a for which the equation x^4 - 2ax^2 + x + a^2 - a = 0 has all its roots real.

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Previous Question: (i) Consider two positive integers a and b which are such that aabb is divisible by 2000. What is the least possible value of the product ab? (ii) Consider two positive integers a and b which are such that abba is divisible by 2000. What is the least possible value of the product ab? Next Question: Let BE and CF be the altitudes of an acute triangle ABC, with E on AC and F on AB. Let O be the point of intersection of BE and CF. Take any line KL through O with K on AB and L on AC. Suppose M and N are located on BE and CF respectively, such that KM is perpendicular to BE and LN is perpendicular to CF. Prove that FM is parallel to EN.

(#M40021950) MATHS OLYMPIAD question ALGEBRA Keep an EYE

Find all real values of a for which the equation
x^4 - 2ax^2 + x + a^2 - a = 0 has all its roots real.: Asked In Maths Olympiad MAN (11 years ago); Unsolved; Is this Puzzle helpful? (2) (2) Submit Your Solution

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Previous Question: (i) Consider two positive integers a and b which are such that aabb is divisible by 2000. What is the least possible value of the product ab? (ii) Consider two positive integers a and b which are such that abba is divisible by 2000. What is the least possible value of the product ab? Next Question: Let BE and CF be the altitudes of an acute triangle ABC, with E on AC and F on AB. Let O be the point of intersection of BE and CF. Take any line KL through O with K on AB and L on AC. Suppose M and N are located on BE and CF respectively, such that KM is perpendicular to BE and LN is perpendicular to CF. Prove that FM is parallel to EN.

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