Find the value of k for which `x=2` is a root (solution) of equation `kx^(2)+2x-3=0`.

Answer

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

### Step 1: Substitute \( x = 2 \) into the equation
Since \( x = 2 \) is a root of the equation, we can substitute \( x \) with \( 2 \) in the equation:

\[ k(2^2) + 2(2) - 3 = 0 \]

### Step 2: Simplify the equation
Now, simplify the equation:

\[ k(4) + 4 - 3 = 0 \]

This simplifies to:

\[ 4k + 4 - 3 = 0 \]

### Step 3: Combine like terms
Combine the constants:

\[ 4k + 1 = 0 \]

### Step 4: Solve for \( k \)
Now, isolate \( k \):

\[ 4k = -1 \]

Dividing both sides by 4 gives:

\[ k = -\frac{1}{4} \]

### Final Answer
Thus, the value of \( k \) for which \( x = 2 \) is a root of the equation \( kx^2 + 2x - 3 = 0 \) is:

\[ \boxed{-\frac{1}{4}} \]

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