Question

Show that x^2 + 2x + 5 is positive for all real values of x ​

Answer 1

Explanation:

x²+2x+5

=x²+2x+1+4

=(x+1)²+4

≥ 4

∀ real x

Hence x²+2x+5 ≥ 4≥0

Hence it is always positive.