Discriminant Calculator

What is the Discriminant?

The discriminant is a special number that helps us understand the solutions of a quadratic equation. It's like a magic key that unlocks the secrets of the equation! The discriminant tells us how many real solutions the equation has and what kind they are.

How to Calculate the Discriminant

To find the discriminant, we use the coefficients of our quadratic equation. It's like following a recipe - we mix the numbers in a special way to get our result!

Formula

For a quadratic equation in the form \(ax^2 + bx + c = 0\), the discriminant is given by:

\[ \Delta = b^2 - 4ac \]

Where:

• \(a\) is the coefficient of \(x^2\)
• \(b\) is the coefficient of \(x\)
• \(c\) is the constant term
• \(\Delta\) (delta) represents the discriminant

Calculation Steps

1. Identify the values of \(a\), \(b\), and \(c\) in your quadratic equation
2. Square the value of \(b\) to get \(b^2\)
3. Multiply \(a\) and \(c\)
4. Multiply the result from step 3 by 4
5. Subtract the result from step 4 from \(b^2\)
6. The final result is your discriminant!

Example and Visual Representation

Let's solve \(x^2 - 5x + 6 = 0\)

1. Here, \(a = 1\), \(b = -5\), and \(c = 6\)
2. \(\Delta = (-5)^2 - 4(1)(6)\)
3. \(\Delta = 25 - 24 = 1\)

The positive discriminant (1) tells us there are two real solutions!