X 2 − 5 x + 4 = 0 x 2 −5x+4=0 ?

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 this equation, the coefficients are:

• \( a = 1 \)
• \( b = -5 \)
• \( c = 4 \)

Now, let's plug these values into the quadratic formula:

1. Calculate the discriminant (\( b^2 - 4ac \)): \[ b^2 - 4ac = (-5)^2 - 4(1)(4) = 25 - 16 = 9 \]

2. Substitute into the quadratic formula: \[ x = \frac{5 \pm \sqrt{9}}{2(1)} = \frac{5 \pm 3}{2} \]

This gives us two solutions:

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

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