### Home > PC3 > Chapter 4 > Lesson 4.1.1 > Problem4-15

4-15.

​ 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?

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.

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.

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