Find the value of K for which `x=2` is a root of the equation `3x^(2)-2Kx+5=0`.

Answer

To find the value of \( K \) for which \( x = 2 \) is a root of the equation \( 3x^2 - 2Kx + 5 = 0 \), we can follow these steps:

### Step 1: Substitute the value of \( x \)
Since we know that \( x = 2 \) is a root of the equation, we substitute \( x = 2 \) into the equation:
\[ 3(2^2) - 2K(2) + 5 = 0 \]

### Step 2: Calculate \( 2^2 \)
Calculate \( 2^2 \):
\[ 2^2 = 4 \]
Now substitute this back into the equation:
\[ 3(4) - 2K(2) + 5 = 0 \]

### Step 3: Simplify the equation
Now simplify the equation:
\[ 12 - 4K + 5 = 0 \]
Combine like terms:
\[ 17 - 4K = 0 \]

### Step 4: Isolate \( K \)
Now, isolate \( K \) by moving \( 17 \) to the other side:
\[ -4K = -17 \]
Now divide both sides by \(-4\):
\[ K = \frac{17}{4} \]

### Conclusion
Thus, the value of \( K \) for which \( x = 2 \) is a root of the equation is:
\[ K = \frac{17}{4} \]

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