To solve the quadratic equation \( x^2 - 5x + 4 = 0 \), we can use factoring. Let's break it down:

1. Start with the equation:
   \[
   x^2 - 5x + 4 = 0
   \]

2. Look for two numbers that multiply to give \( 4 \) (the constant term) and add up to \( -5 \) (the coefficient of \( x \)).

   These numbers are \( -4 \) and \( -1 \), because:
   \[
   (-4) \times (-1) = 4 \quad \text{and} \quad (-4) + (-1) = -5
   \]

3. Now factor the quadratic:
   \[
   (x - 4)(x - 1) = 0
   \]

4. Set each factor equal to zero:
   \[
   x - 4 = 0 \quad \text{or} \quad x - 1 = 0
   \]

5. Solve for \( x \):
   \[
   x = 4 \quad \text{or} \quad x = 1
   \]

Thus, the solutions to the equation \( x^2 - 5x + 4 = 0 \) are:
\[
x = 4 \quad \text{and} \quad x = 1
\]

Would you like any more details on this solution or any further explanations?

Here are 5 related questions you can explore:
1. How can you solve a quadratic equation using the quadratic formula?
2. What are the applications of quadratic equations in real-life problems?
3. How can you check if the roots of a quadratic equation are real or complex?
4. What happens when the discriminant of a quadratic equation is zero?
5. How can you solve quadratic equations graphically?

**Tip**: Always verify your solution by plugging the values of \(x\) back into the original equation to check if they satisfy it!

Learn how to solve the quadratic equation x² - 5x + 4 using factoring. This detailed step-by-step guide explores key algebraic concepts, such as factoring and the Zero Product Property. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation