The sum of the roots of quadratic equation `2x+4/x=9` is

Options

A. `7/2`
B. `9/2`
C. 3
D. `-9/2`

Answer

To find the sum of the roots of the quadratic equation given by \( 2x + \frac{4}{x} = 9 \), we can follow these steps:

### Step 1: Rewrite the equation
Start with the original equation:
\[ 2x + \frac{4}{x} = 9 \]

### Step 2: Eliminate the fraction
To eliminate the fraction, multiply the entire equation by \( x \) (assuming \( x \neq 0 \)):
\[ x(2x) + x\left(\frac{4}{x}\right) = 9x \]
This simplifies to:
\[ 2x^2 + 4 = 9x \]

### Step 3: Rearrange into standard quadratic form
Rearranging the equation gives:
\[ 2x^2 - 9x + 4 = 0 \]

### Step 4: Identify coefficients
In the standard form \( ax^2 + bx + c = 0 \), we identify:
- \( a = 2 \)
- \( b = -9 \)
- \( c = 4 \)

### Step 5: Use the formula for the sum of the roots
The sum of the roots of a quadratic equation is given by the formula:
\[ \text{Sum of roots} = -\frac{b}{a} \]
Substituting the values of \( b \) and \( a \):
\[ \text{Sum of roots} = -\frac{-9}{2} = \frac{9}{2} \]

### Final Answer
Thus, the sum of the roots of the quadratic equation is:
\[ \frac{9}{2} \]

---