You have the expression:  
\[
- x^2 + 6x - 4
\]

This is a quadratic expression, and it can be analyzed or solved in various ways. Let me know which of the following you'd like to explore:

1. **Factoring** (if possible)  
2. **Finding the roots using the quadratic formula**  
3. **Completing the square**  
4. **Graphing the equation**  
5. **Analyzing the vertex and axis of symmetry**

To proceed, let's find the **roots** using the quadratic formula. The general quadratic formula is:

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

In your expression, \(a = -1\), \(b = 6\), and \(c = -4\).

### Step 1: Calculate the discriminant
\[
\Delta = b^2 - 4ac = 6^2 - 4(-1)(-4) = 36 - 16 = 20
\]

### Step 2: Apply the quadratic formula
\[
x = \frac{-6 \pm \sqrt{20}}{2(-1)} = \frac{-6 \pm 2\sqrt{5}}{-2}
\]

### Step 3: Simplify the expression
\[
x = 3 \mp \sqrt{5}
\]

Thus, the roots of the equation are:
\[
x_1 = 3 + \sqrt{5}, \quad x_2 = 3 - \sqrt{5}
\]

Would you like further details on this solution? 

Here are five questions to expand on this:

1. Would you like to graph this quadratic expression?
2. Do you want to explore how to complete the square for this expression?
3. Would you like to factor a similar quadratic equation?
4. Are you interested in the vertex form of this quadratic expression?
5. Would you like to analyze how the discriminant affects the nature of the roots?

**Tip:** The discriminant, \(b^2 - 4ac\), determines the type of roots. If it’s positive, the roots are real and distinct.

This webpage provides a detailed step-by-step guide to solving the quadratic equation -x² + 6x - 4. The solution includes calculating the discriminant, using the quadratic formula, and analyzing the roots. Ideal for students in Grades 8-10 learning algebraic concepts like discriminants and quadratic equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation