... 1. Find conditions on a, b, c (assuming a ≠ c) so that p(x) and q(x) have two common roots. In this case solve p(x) = q(x) = 0. A2. The diagram shows a network of roads. The distance from one ... It is possible to find 10 agents such that the first watches the second, the second watches the third, , and the tenth watches the first. Show that it is possible to find a cycle of 11 such ... triangle ABC, show how to find geometrically the point P such that ∠PAB = ∠PBC = ∠PCA. Express this angle in terms of ∠A, ∠B, ∠C using trigonometric functions. B3. For each positive integer...