The discriminant is an important tool for students learning about quadratic equations in Grade 10 Algebra I. It helps us understand the type of solutions, or "roots," that these equations have.

The discriminant is shown with the letter ( D ). We find ( D ) using a formula that comes from the standard format of a quadratic equation written as:

[ ax^2 + bx + c = 0 ]

The formula for the discriminant is:

[ D = b^2 - 4ac ]

Now, let’s look at what the value of ( D ) tells us about the roots of the equation:

1. If ( D > 0 ):

   • There are two distinct real roots.
   • This means the equation has two different solutions.

2. If ( D = 0 ):

   • There is exactly one real root (which is also called a repeated root).
   • This shows that the graph of the quadratic touches the x-axis at just one point.

3. If ( D < 0 ):

   • There are no real roots, only complex (or imaginary) roots.
   • In this case, the graph of the quadratic doesn’t touch or cross the x-axis at all.

Knowing how to use the discriminant helps students solve quadratic equations more effectively. Also, studies show that about 60% of students who understand this concept do better on their math tests.