+9466 Find the least value of b such that b2+ 2b - 15 ≤ 0 .
First let's find what value of b makes
b2+ 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.
02 + 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
