To solve the quadratic equation \(x^2 - 6.4x + 2.5 = 0\), we can use Vieta's formulas. According to Vieta's formulas, for a quadratic equation of the form \(ax^2 + bx + c = 0\):
- The sum of the roots \(x_1 + x_2 = -\frac{b}{a}\)
- The product of the roots \(x_1 \cdot x_2 = \frac{c}{a}\)
In this case, we have:
- \(a = 1\)
- \(b = -6.4\)
- \(c = 2.5\)
Now, using Vieta's formulas:
Sum of the roots: \[ x_1 + x_2 = -\frac{-6.4}{1} = 6.4 \]
Product of the roots: \[ x_1 \cdot x_2 = \frac{2.5}{1} = 2.5 \]
So, the values are:
- \(x_1 + x_2 = 6.4\)
- \(x_1 \cdot x_2 = 2.5\)