To solve the quadratic equation \( x^2 - 5x + 4 = 0 \), we can use the **quadratic formula**:

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

In the given equation, \( a = 1 \), \( b = -5 \), and \( c = 4 \). Let's plug these values into the formula:

\[
x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(4)}}{2(1)}
\]
\[
x = \frac{5 \pm \sqrt{25 - 16}}{2}
\]
\[
x = \frac{5 \pm \sqrt{9}}{2}
\]
\[
x = \frac{5 \pm 3}{2}
\]

So, the two possible solutions are:

1. \( x = \frac{5 + 3}{2} = \frac{8}{2} = 4 \)
2. \( x = \frac{5 - 3}{2} = \frac{2}{2} = 1 \)

Thus, the solutions are:

\[
x = 4 \quad \text{or} \quad x = 1
\]

Would you like further explanation or details on this?

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Here are 5 related questions:
1. What are the different methods to solve quadratic equations?
2. How can we factor \(x^2 - 5x + 4\) without using the quadratic formula?
3. What are the conditions for a quadratic equation to have real solutions?
4. How does the discriminant affect the type of solutions of a quadratic equation?
5. What are the applications of quadratic equations in real life?

**Tip:** Always check the discriminant \(b^2 - 4ac\) before solving, as it tells you the nature of the roots (real, repeated, or complex).

Learn how to solve the quadratic equation x² - 5x + 4 = 0 step by step using the quadratic formula. This guide explains the core algebraic concepts, including the discriminant and quadratic formula, and is suitable for students in Grades 8-10.

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