Question 416358
I would use the fact that the minimum on the graph is at {{{-b/(2a)}}}
when the form is {{{ax^2 + bx + c}}}, so min = {{{-7/2}}}
The roots will be on either side of this. You can try
(1)  {{{x = -4}}} and{{{x = -3}}}. 
Then try
(2)  {{{x = -5}}} and {{{x = -2}}}, 
next
(3) {{{x = -6}}} and {{{x = -1}}}
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Here's the graph:
{{{ graph( 400, 400, -8, 3, -4, 10, x^2 + 7x + 9) }}}
You can see that {{{y}}} will change sign when you go
from choice (2) to choice (3) above