18

Part of 2018 Purple Comet Problems

Problems(2)

Purple Comet 2018 MS problem 18

Source:

ABCD

has side lengths

AB = 6\sqrt3

BC = 8\sqrt3

. The probability that a randomly chosen point inside the rectangle is closer to the diagonal

\overline{AC}

than to the outside of the rectangle is

\frac{m}{n}

m

n

are relatively prime positive integers. Find

m + n

geometryprobability

Purple Comet 2018 HS problem 18

Source:

Find the positive integer

k

such that the roots of

x^3 - 15x^2 + kx -1105

are three distinct collinear points in the complex plane.

complex numberspolynomial