Question

Solve the inequality -x^2-4x+5>0

Answer 1

−x2−4x+5>0
Let's find the critical points of the inequality.
−x2−4x+5=0
(−x+1)(x+5)=0(Factor left side of equation)
−x+1=0 or x+5=0(Set factors equal to 0)
x=1 or x=−5
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<−5(Doesn't work in original inequality)
−5<x<1(Works in original inequality)
x>1(Doesn't work in original inequality)
Answer: −5<x<1