Question 476572
<pre>
The expression (x-5)(x-4) is a quadratic with two zeros, 4 and 5.

So there are three open intervals to test on each side of and between
the two zeros to determine whether on them the expression is always 
greater than or always less than 0.

{{{matrix(1,6,

(matrix(1,3,-infinity,",",4)),
",",
(matrix(1,3,4,",",5)), 
",", 
and,
(matrix(1,3,5,",",infinity))

)}}}

Choose easiest test point x=0 on {{{(matrix(1,3,-infinity,",",4))}}}
(0-5)(0-4) = 20 Thus the expression is greater 
than 0 on this interval.  So we will use it with the zero 4

Choose easiest test point x=4.5 on {{{(matrix(1,3,4,",",5))}}}
(4.5-5)(4.5-4) = -0.25 Thus the expression is less 
than 0 on this interval.  Thus we will not use it.

Choose easiest test point x=6 on {{{(matrix(1,3,5,",",infinity))}}}
(6-5)(6-4) = 2 Thus the expression is greater 
than 0 on this interval.  So we will use it with the zero 5

Answer: The expression is greater than 0 on 

{{{matrix(1,3,

matrix(1,5,"(",-infinity,",",4,"]"),
U,
matrix(1,5,"[",5,",",infinity,")")

)}}}




Edwin</pre>