To find the discriminant of a quadratic equation, you need to identify the equation in the standard form:

\[
ax^2 + bx + c = 0
\]

The discriminant \( \Delta \) is given by the formula:

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

Where:
- \( a \) is the coefficient of \( x^2 \),
- \( b \) is the coefficient of \( x \),
- \( c \) is the constant term.

The discriminant helps to determine the nature of the roots:
- If \( \Delta > 0 \), the equation has two distinct real roots.
- If \( \Delta = 0 \), the equation has one real root (a repeated root).
- If \( \Delta < 0 \), the equation has two complex roots.

### Example:

For the quadratic equation \( 2x^2 - 4x + 3 = 0 \), the coefficients are:
- \( a = 2 \),
- \( b = -4 \),
- \( c = 3 \).

Using the formula for the discriminant:

\[
\Delta = (-4)^2 - 4(2)(3) = 16 - 24 = -8
\]

Thus, \( \Delta = -8 \), so the equation has two complex roots.

---

Do you have a specific quadratic equation you would like me to help with? Feel free to upload a photo of the equation if needed!

### Relative Questions:
1. What does it mean if the discriminant is negative?
2. Can the discriminant be applied to other types of polynomials?
3. How does the discriminant relate to the graph of a quadratic function?
4. How can you factor a quadratic if the discriminant is a perfect square?
5. What is the geometric significance of the discriminant?

**Tip:** The discriminant helps you decide whether a quadratic equation is factorable or not without solving it entirely.

Learn how to calculate the discriminant of a quadratic equation using the formula Δ = b^2 - 4ac. This step-by-step guide explains the process, the significance of the discriminant, and provides an example with complex roots. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation