Answer: [tex]\boxed{\left(c-\frac{5}{2}-\frac{i\sqrt{11}}{2} \right)\left(c-\frac{5}{2}+\frac{i\sqrt{11}}{2} \right)}[/tex]
Step-by-step explanation:
Using the quadratic formula to find the roots of the equation,
[tex]c=\frac{-(-5) \pm \sqrt{(-5)^2 -4(1)(9)}}{2(1)}\\\\c=\frac{5}{2} \pm \frac{i\sqrt{11}}{2}[/tex]
So,
[tex]c^2 -5c+9=\boxed{\left(c-\frac{5}{2}-\frac{i\sqrt{11}}{2} \right)\left(c-\frac{5}{2}+\frac{i\sqrt{11}}{2} \right)}[/tex]
