Sum of roots of quadratic equation `x^(2) - 4x + 2 =0` is ………of product of roots .

Answer

To solve the problem, we need to find the sum and product of the roots of the quadratic equation \( x^2 - 4x + 2 = 0 \) and then determine the relationship between them.

### Step 1: Identify the coefficients
The given quadratic equation is in the standard form \( ax^2 + bx + c = 0 \).
Here, we have:
- \( a = 1 \)
- \( b = -4 \)
- \( c = 2 \)

### Step 2: Calculate the sum of the roots
The sum of the roots (denoted as \( \alpha + \beta \)) of a quadratic equation can be calculated using the formula:
\[ \alpha + \beta = -\frac{b}{a} \]
Substituting the values of \( b \) and \( a \):
\[ \alpha + \beta = -\frac{-4}{1} = \frac{4}{1} = 4 \]

### Step 3: Calculate the product of the roots
The product of the roots (denoted as \( \alpha \beta \)) can be calculated using the formula:
\[ \alpha \beta = \frac{c}{a} \]
Substituting the values of \( c \) and \( a \):
\[ \alpha \beta = \frac{2}{1} = 2 \]

### Step 4: Determine the relationship
Now we need to find out how many times the sum of the roots is of the product of the roots. We have:
- Sum of roots \( \alpha + \beta = 4 \)
- Product of roots \( \alpha \beta = 2 \)

To find how many times the sum is of the product:
\[ \text{Ratio} = \frac{\alpha + \beta}{\alpha \beta} = \frac{4}{2} = 2 \]

### Conclusion
The sum of the roots of the quadratic equation \( x^2 - 4x + 2 = 0 \) is **2 times** the product of the roots.

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