Strategy 1: Use the standard quadratic formula:
[tex]ax^2+bx+c=0 \iff x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In your case, [tex]a=1,\ b=4,\ c=5[/tex], so we have
[tex]x_{1,2} = \dfrac{-4\pm\sqrt{16-20}}{2}[/tex]
Since the expression involves the square root of a negative value, the function has no (real) zeroes.
