# 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 x-axis, touches the x-axis, or does not intersect the x-axis 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.