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Re: HSC 2013 4U Marathon Let P(x)=x^5-5cx+1 where c is real 1) If c<0, prove that P has exactly one real root and that it is negative 2) Prove that if P has exactly 3 distinct real roots, then c>(1/4)^(4/5)

Re: HSC 2013 4U Marathon Let the point of concurrency be G. We can use the following theorem: Thm: If you have a triangle ABC with D on the interior of BC. Then ABD/ACD=BD/CD. (This is because if you let the height from A be h. Then ABD=h(BD) and ACD=h(CD).) So, BD/CD=ABD/ACD=BGD/CGD. if...

Re: HSC 2013 4U Marathon For what it's worth, here's how I did it. Alice has n+1 tosses. Bob has n tosses. Define winning in the following way. Alice wins if she gets more heads than Bob. Bob wins if she does not. Bob wins if and only if Alice throws more tails than Bob Alice wins if and only...