To solve the quadratic equation \( 3x^2 + 2x - 1 = 0 \), we can use the **quadratic formula**:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, the coefficients are:
- \( a = 3 \)
- \( b = 2 \)
- \( c = -1 \)

### Step 1: Plug the values into the quadratic formula:
\[
x = \frac{-2 \pm \sqrt{2^2 - 4(3)(-1)}}{2(3)}
\]

### Step 2: Simplify inside the square root:
\[
x = \frac{-2 \pm \sqrt{4 + 12}}{6}
\]
\[
x = \frac{-2 \pm \sqrt{16}}{6}
\]
\[
x = \frac{-2 \pm 4}{6}
\]

### Step 3: Solve for both values of \( x \):

1. \( x_1 = \frac{-2 + 4}{6} = \frac{2}{6} = \frac{1}{3} \)
2. \( x_2 = \frac{-2 - 4}{6} = \frac{-6}{6} = -1 \)

### Final Answer:
The solutions are:
\[
x_1 = \frac{1}{3}, \quad x_2 = -1
\]

Would you like more details on how the quadratic formula works or why we use it here?

Here are 5 related questions you can explore:
1. What is the discriminant in a quadratic equation, and how does it affect the solution?
2. How would you solve a quadratic equation by factoring?
3. What is the vertex form of a quadratic equation?
4. How can you graph \( 3x^2 + 2x - 1 \), and what are its key features?
5. How does completing the square help in solving quadratic equations?

**Tip**: Always check the discriminant \( b^2 - 4ac \) first, as it tells you if the solutions will be real or complex.

This tutorial demonstrates how to solve the quadratic equation 3x^2 + 2x - 1 = 0 using the quadratic formula. It covers key algebraic concepts and provides a detailed step-by-step breakdown 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