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Consider the polynomial P(x)=x4-x3+x. Prove that for every positive real number a, the polynomial Qa(x)=P(x)-a has exactly one positive root.
(No Solution Yet, 1 Comments) Submitted on 2025-06-04 by Danish Ahmed Khan   
Difficulty: 3 of 5 Bonus: Prime = Sqrt of Summed Primes (in Numbers) Rating: 2.00
(No Solution Yet, 6 Comments) Submitted on 2011-03-06 by brianjn   
Difficulty: 1 of 5Largest number divisible by 18 (in Numbers)
Posted on 2025-06-04 by Danish Ahmed Khan (No Solution Yet, 3 Comments)
Difficulty: 2 of 5A tangent tale (in Geometry)
Posted on 2025-06-03 by Danish Ahmed Khan (No Solution Yet, 0 Comments)
Difficulty: 3 of 5Same Base, Same Area (in Geometry)
Posted on 2025-06-03 by Charlie (No Solution Yet, 1 Comments)
Difficulty: 2 of 5Concat Sequence - duplicate digits (in Numbers)
Posted on 2025-06-02 by Larry (No Solution Yet, 1 Comments)
Difficulty: 3 of 5Probability with sum of digits (in Probability)
Posted on 2025-06-02 by Danish Ahmed Khan (No Solution Yet, 2 Comments)
Difficulty: 2 of 5Fill in the Blanks 3 (in Word Problems)
Posted on 2025-06-01 by Charlie (No Solution Yet, 1 Comments)
Difficulty: 3 of 5Parallelogram extension (in Geometry)
Posted on 2025-05-31 by Danish Ahmed Khan (No Solution Yet, 1 Comments)
Difficulty: 3 of 5How much is that in Terran money? (in Numbers) Rating: 5.00
Posted on 2025-05-30 by broll (No Solution Yet, 5 Comments)
Difficulty: 3 of 5Equilateral and Isosceles (in Geometry)
Posted on 2025-05-30 by Danish Ahmed Khan (No Solution Yet, 1 Comments)
Difficulty: 4 of 5Daylight Map (in Geometry)
Posted on 2025-05-29 by Charlie (Solution Posted, 0 Comments)
Difficulty: 2 of 5Cubic summation (in Just Math) Rating: 2.00
Posted on 2025-05-29 by Danish Ahmed Khan (No Solution Yet, 1 Comments)
Difficulty: 3 of 5Segment in circle (in Geometry)
Posted on 2025-05-28 by Danish Ahmed Khan (No Solution Yet, 1 Comments)
Difficulty: 3 of 5Square inequality (in Just Math)
Posted on 2025-05-28 by Danish Ahmed Khan (No Solution Yet, 3 Comments)
Difficulty: 3 of 5Locus in quarter (in Geometry)
Posted on 2025-05-27 by Danish Ahmed Khan (No Solution Yet, 1 Comments)

Recently Posted Solutions:
Difficulty: 4 of 5Daylight Map (in Geometry)
Submitted By Charlie. Solution posted on 2025-06-01 18:11:33
Difficulty: 3 of 5Pick Up More Sticks (in Just Math)
Submitted By Larry. Solution posted on 2025-05-27 12:26:17
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Submitted By Charlie. Solution posted on 2025-05-08 10:56:00
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Submitted By Larry. Solution posted on 2025-05-07 14:15:21
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