​ Consider the quadratic equation $x^2-10x+29=0$.  

1. Is $x=5+2i$ a solution to the equation? How can you be sure without solving?

   Hint (a):

   Substitute it into the equation.

   $(5 + 2i)^2 - 10(5 + 2i) = -29\text{ ?}$ 

2. Without solving, predict another solution to the equation. Verify your prediction by checking it.

   Hint (b):

   Review the solutions to the equation in problem 4-8.

3. Where does the parabola $y=x^2-10x+29$ intersect the $x$-axis? Explain.

   Hint (c):

   The roots are complex numbers.
   Note: You can graph the function on a calculator to check.