Question

solve the inequality : -x^2+2x+15>0

Answer 1

@jazzie

Answer 2

we first factorize the quadratic
\[
-x^2+2x+15>0\\
-(x^2-2x-15)>0\\
-(x^2-5x+3x-15)>0\\
-(x-5)(x+3)>0\\
(5-x)(x-3)>0
\]
now,
when is the product of two numbers positive?
1) when both are positive OR
2) both are negative

Answer 3

wouldnt my answer be x<-3 or x>5

Answer 4

the first contition gives us:
\[5-x>0\qquad{\rm AND}\qquad x+3>0\\
5>x\qquad{\rm AND}\qquad x>-3\\
\boxed{-3<x<5}
\]
from the second condition:
\[
5-x<0\qquad{\rm AND}\qquad x+3<0\\
5<x\qquad{\rm AND}\qquad x<-3\\
\boxed{x\in(-\infty,-3)\cup(5,\infty)}
\]

Answer 5

thanks so much!!!

Answer 6

yw.