The Discriminant
Understanding the Discriminant

The discriminant is a key component in the quadratic formula and gives important information about the nature of the roots of a quadratic equation.

The discriminant is derived from the equation b²  4ac in the quadratic formula.
Function of the Discriminant
 The discriminant gives information about the roots of a quadratic equation without having to solve the equation.
 The nature and number of roots of a quadratic equation can be determined by the sign and value of the discriminant.
Interpreting the Discriminant

Positive Discriminant: If the discriminant is positive, it indicates that the quadratic equation has two distinct real roots.

Zero Discriminant: If the discriminant is zero, it implies that the quadratic equation has one real root, also known as a repeated root.

Negative Discriminant: If the discriminant is negative, it signifies that the quadratic equation has no real roots but two complex roots instead.
Applying the Discriminant
 The discriminant can be used to identify the type of roots in higher degree polynomials by considering the quadratic factors.
 The discriminant helps to draw conclusions about geometric properties of the graph of a quadratic function, such as whether the parabola intersects the xaxis, touches the xaxis, or does not intersect the xaxis at all.
Remember, using the discriminant is a quick way to assess the nature of the roots of a quadratic equation without actually solving the equation for its roots.