Discriminant facts for kids

The discriminant is a special number that helps us understand the solutions of certain math problems, especially equations called polynomials. It's often shown with the symbol , which is a Greek letter called Delta.

Think of it like a secret code that tells you how many answers an equation has.

What is a Polynomial?

A polynomial is a math expression made of variables (like x) and numbers, using only addition, subtraction, multiplication, and non-negative whole number powers of the variable (like x² or x³).

The Discriminant for Quadratic Equations

The most common place you'll see the discriminant is with a quadratic equation. This is a polynomial where the highest power of x is 2. It looks like this:

Here, a, b, and c are just numbers. The discriminant for this type of equation is calculated using a simple formula:

What the Discriminant Tells You

Once you calculate the discriminant (), its value tells you about the solutions (or "roots") of the quadratic equation:

• If the discriminant is greater than zero (Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \Delta > 0 ): The equation has two different real solutions. Real numbers are the numbers you usually work with, like 1, -5, 0.5, or .
• If the discriminant is equal to zero (Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \Delta = 0 ): The equation has exactly one real solution. This solution is sometimes called a "repeated root" because it appears twice.
• If the discriminant is less than zero (Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \Delta < 0 ): The equation has two complex solutions. Complex numbers are a different kind of number that involve the square root of negative one. You usually learn about them in higher-level math.

Beyond Quadratic Equations

While the discriminant is most often taught with quadratic equations, it can also be defined for other types of polynomials, like cubic polynomials (where the highest power of x is 3), and even for other mathematical ideas. The formulas for these are usually more complicated.

Related pages

• Equation solving
• Quadratic equation

Images for kids

• 

  This image shows the zero set of the discriminant for cubic polynomials. It's where the discriminant equals zero.

• 

  This image shows the discriminant for a quartic polynomial (where the highest power of x is 4). The surface shows points where the polynomial has repeated solutions.

See also

In Spanish: Discriminante para niños