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

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

Here, \( a = 1 \), \( b = -5 \), and \( c = 4 \). Substituting these values into the quadratic formula:

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

So, the two solutions are:

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

Thus, the solutions are \( y = 4 \) and \( y = 1 \).

Would you like more details or have any questions? Here are 5 related questions to explore:

1. How can we graph the quadratic equation \( y^2 - 5y + 4 = 0 \)?
2. What is the significance of the discriminant in a quadratic equation?
3. How do you derive the quadratic formula?
4. How can we factor the quadratic equation \( y^2 - 5y + 4 \)?
5. What are the roots of a quadratic function?

**Tip:** Always check the discriminant \( b^2 - 4ac \) to determine the nature of the roots (real or complex).

Learn how to solve the quadratic equation y^2 - 5y + 4 = 0 with a detailed step-by-step solution. Understand the quadratic formula application and find the roots of the equation. Suitable for high school students studying algebra.

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