Solve inequality and put solution set in interval notation.

Question

z^2+2z+6>0

Answer 1

z^2+2z + 1 +5>0
(z+1)^2> -5
Which has no real solutions.

take square root of each side
z+1 < isqrt5 but sqrt5 has two roots, so

-isqrt5<z+1<+isqrr5

subtract 1 from all sides, and you have it.

-1-isqrt5<z<-1+isqrt5

I am surprised your teacher gave you this, as I suspect it is a little over your experience level. If the 6 had been -6, it would be different.

Answer 2

Actually, (z-1)^2 >= 0, so it is > -5 for all x!