beero1000
Veteran Member
For those interested (or bored) enough, a new thread to pose/solve math problems.
- Suppose the roots of the polynomial x5 + 2x4 + 3x3 + 4x2 + 5x + 6 are a, b, c, d, and e, respectively. Find a2+b2+c2+d2+e2. Bonus points: Find the harmonic mean of the roots (i.e. 5 times the reciprocal of the sum of their reciprocals).
- An irregular octagon is inscribed in a circle. The edge lengths of the octagon are 4,4,4,4,2,2,2,2. Find the area of the octagon. Bonus points: Find the radius of the circle.
- Is (14n+3)/(21n + 4) a fraction in simplest form for every n?
- Two unit circles pass through each other's center. Find the area of their intersection. Bonus points: Same question for 3 intersecting circles.