Discriminant

Definition

The discriminant is a value calculated from the coefficients of a quadratic equation $ax^2 + bx + c = 0$. It determines the nature and number of roots of the quadratic equation.

5 Must Know Facts For Your Next Test

1. The discriminant is given by the formula $D = b^2 - 4ac$.
2. If $D > 0$, the quadratic equation has two distinct real roots.
3. If $D = 0$, the quadratic equation has exactly one real root (a repeated root).
4. If $D < 0$, the quadratic equation has two complex conjugate roots.
5. The discriminant provides insight into whether the parabola corresponding to the quadratic equation intersects, touches, or does not intersect the x-axis.

Review Questions

• What is the formula for calculating the discriminant of a quadratic equation?
• What does it mean for a quadratic equation if its discriminant is zero?
• How many real roots does a quadratic equation have if its discriminant is negative?

Related terms

Quadratic Equation:

A polynomial equation of degree two in the form $ax^2 + bx + c = 0$.

Real Roots:

Solutions to a polynomial equation that are real numbers.

Complex Conjugate Roots: A pair of complex numbers, each with equal real parts and imaginary parts that are equal in magnitude but opposite in sign.