Discriminant

Definition

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by the expression $b^2 - 4ac$. It determines the nature and number of roots of the quadratic equation.

5 Must Know Facts For Your Next Test

1. The discriminant is found using the formula $b^2 - 4ac$.
2. If the discriminant is greater than zero, the quadratic equation has two distinct real roots.
3. If the discriminant equals zero, the quadratic equation has exactly one real root (a repeated root).
4. If the discriminant is less than zero, the quadratic equation has two complex conjugate roots.
5. The value of the discriminant can help determine whether a quadratic function's graph intersects the x-axis.

Review Questions

• What is the formula for calculating the discriminant?
• How do you interpret a negative discriminant in terms of roots?
• What does it mean if a quadratic equation has a discriminant of zero?

Related terms

Quadratic Equation: An equation in which the highest power of an unknown variable is squared, typically in the form $ax^2 + bx + c = 0$.

Roots: Solutions to an equation where it equals zero. In quadratics, these can be real or complex numbers determined by the discriminant.

$b^2 - 4ac$: The mathematical expression used to calculate the discriminant of a quadratic equation.