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The image contains a problem in Chinese that seems to involve solving for the roots of a quadratic equation and other related tasks. The problem appears to be in multiple parts. Here's a breakdown:

1. **Find the value of \(\alpha + \beta\)** where \(\alpha\) and \(\beta\) are the roots of the given quadratic equation.
2. **Find the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\)**.
3. **Using \(\alpha\) and \(\beta\), derive the general form of a quadratic equation** using a given formula.

Given the equation \(2x^2 - x + 1 = 0\), let's solve each part step by step:

### Part 1: Finding \(\alpha + \beta\)
For a quadratic equation of the form \(ax^2 + bx + c = 0\), the sum of the roots \(\alpha + \beta\) is given by:
\[
\alpha + \beta = -\frac{b}{a}
\]
For the equation \(2x^2 - x + 1 = 0\), we have \(a = 2\) and \(b = -1\). Thus:
\[
\alpha + \beta = -\frac{-1}{2} = \frac{1}{2}
\]

### Part 2: Finding \(\frac{1}{\alpha} + \frac{1}{\beta}\)
We can use the relationship:
\[
\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha \beta}
\]
For a quadratic equation, the product of the roots \(\alpha \beta\) is given by:
\[
\alpha \beta = \frac{c}{a}
\]
For the equation \(2x^2 - x + 1 = 0\), \(a = 2\) and \(c = 1\), so:
\[
\alpha \beta = \frac{1}{2}
\]
Now, substituting the values found:
\[
\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\frac{1}{2}}{\frac{1}{2}} = 1
\]

### Part 3: Deriving the quadratic equation
Using the formula given in the problem, likely \(y = a(x - \alpha)(x - \beta)\), we substitute the values for \(\alpha\) and \(\beta\). We can express the quadratic equation in terms of its roots:
\[
y = 2(x - \alpha)(x - \beta)
\]
Given the roots are \(\alpha\) and \(\beta\), we could factor the quadratic equation back into its standard form. Without specific values for \(\alpha\) and \(\beta\), this process would typically just reverse the original quadratic formula.

If you need further details or have any questions, feel free to ask! Here are some related questions you might consider:

1. What are other methods for solving quadratic equations?
2. How can the discriminant be used to determine the nature of the roots?
3. What happens if the quadratic equation has complex roots?
4. How do you solve a quadratic equation using the quadratic formula?
5. Can we use a graphical method to find the roots of a quadratic equation?

**Tip:** Understanding the relationship between the coefficients of a quadratic equation and its roots is crucial for efficiently solving such problems.

Explore how to solve the quadratic equation 2x^2 - x + 1 = 0 step-by-step. This problem involves finding the sum and product of roots, deriving the general form of a quadratic equation, and applying relevant formulas. Suitable for high school students.

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