Hi
BunuelI read this post of yours and it was extremely helpful. However I'm a little confused, it'll be great if you can help me out here. So in this post, it says that if the sign is "<", it means that x lies between the 2 roots and if the sign is ">", then x lies on the left of the smaller root and on the right of the bigger root. Now I was solving this other question -
If x^2 + 2x -15 = -m, where x is an integer from -10 and 10, inclusive, what is the probability that m is greater than zero?
A. 2/7
B. 1/3
C. 7/20
D. 2/5
E. 3/7
Re-arrange the given equation: −x^2−2x+15=m
Given that xx is an integer from -10 and 10, inclusive (21 values) we need to find the probability that −x^2−2x+15 is greater than zero, so the probability that −x^2−2x+15>0
Factorize: (x+5)(3−x)>0.
This equation holds true for −5<x<3Since x is an integer then it can take the following 7 values: -4, -3, -2, -1, 0, 1, and 2.
Here, if (x+5)(3−x)>0, then shouldn't x be smaller than -5 and greater than 3? I know that doesn't satisfy the equation given in the question but I was wondering how this was possible if the sign ">" meant that the solution lies on the left of the smaller root and on the right of the bigger root.