What is the formula for a perfect square trinomial and how does the discriminant fit in

The video tutorial covers the quadratic formula, focusing on the discriminant's role in determining the nature of solutions. It explains how the discriminant affects the number and type of solutions, including rational and irrational solutions. The tutorial also revisits previous topics like factoring and completing the square, providing a comprehensive understanding of solving quadratic equations.

Describe what happens when the discriminant is negative.

How do you determine the nature of the solutions based on the value of the discriminant?