Posted by Anonymous on Sunday, December 26, 2010 at 6:30pm.
What your question really asks for is,
"For what values of x does the corresponding parabola
y = x^2 - 3x - 4 fall below the x-axis?"
let's find the x-intercepts ....
x^2 - 3x - 4 = 0
(x-4)(x+1) = 0
x = -1 or x = 4
so the expression is < 0 for -1 < x < 4
or
(x+1)(x-4) < 0
( x+1 >0 AND x-4<0) OR ( x+1 < 0 AND x-4>0)
( x>-1 and x<4) OR (x<-1 AND x > 4)
x>-1 and x<4 OR (null set)
-1 < x < 4
thank you, so anything between -1 and 4 would be my answer? (0,1,2,3)?
yes.
Since your domain is integers, only the integers (0,1,2,3) satisfy the inequality. Otherwise, there would be an infinite number of non-integer solutions between -1 and 4.
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