Bunuel wrote:
Sorry, there was a typo in the stem .
5. 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 \(x\) 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 \(-5<x<3\).
Since x is an integer then it can take the following 7 values: -4, -3, -2, -1, 0, 1, and 2.
So, the probability is 7/21=1/3.
Answer: B.
Hi Bunuel
Could you please check below is fine? Thanks
can we write ? m>0 -----> -x^2-2x+15 > 0
x^2+2x-15 < 0
(x+5)(x-3) < 0
test some big number like 100 --> (x+5)(x-3) will be positive
--- +ve--- -5 ------ -ve------- 3 -----+ve---------
range of x ==> -5<x<3