Asked by Anonymous
if the domain is the set of integers, the solution set of x^2 -3x -4<0 is what?
Answers
Answered by
Reiny
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
"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
Answered by
Anonymous
thank you, so anything between -1 and 4 would be my answer? (0,1,2,3)?
Answered by
bobpursley
yes.
Answered by
drwls
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.