Problem 7

Given the equation =0, find the values of k such that one root of the equation is less than 1; another root is in the interval (1, 4); and the third root is greater than 4.

[Problem submitted by Steve Lee, LACC Professor of Mathematics.]

Solution for Problem 7:

Let f(x)= , then a rough sketch of the graph of f(x) is the following.

(1) or

(2)

k must satisfy both (1) and (2).