MathDB

A real number

a

is chosen randomly and uniformly from the interval

[-20, 18]

. The probability that the roots of the polynomial

x^4 + 2ax^3 + (2a-2)x^2 + (-4a+3)x - 2

are all real can be written in the form

\tfrac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m+n

Problem Statement