#1**+6 **

Find the least value of b such that b^{2}+ 2b - 15 ≤ 0 .

First let's find what value of b makes

b^{2}+ 2b - 15 = 0

Factor it.

(b - 3)(b + 5) = 0

Set each factor equal to zero.

b - 3 = 0 and b + 5 = 0

b = 3 and b = -5

Now to find out what all values of b makes it less than 0,

let's test a point in the middle of -5 and 3, say 0, and see if that makes the inequality true.

0^{2} + 2(0) - 15 ≤ 0

- 15 ≤ 0 true

Just to be safe let's test a point less than -5, say -6, and a point greater than 3, say 4.

36 - 12 - 15 ≤ 0

9 ≤ 0 false

16 + 8 - 15 ≤ 0

9 ≤ 0 false

So all this means that **-5 ≤ b ≤ 3**

hectictar
Mar 19, 2017