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

Answer

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

### Step 1: Substitute \( x = 2 \) into the equation

We start by substituting \( x = 2 \) into the equation:

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

### Step 2: Simplify the equation

Calculating \( 2^2 \) gives us \( 4 \), so we can rewrite the equation:

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

This simplifies to:

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

### Step 3: Further simplify the equation

Now, we simplify \( 4 - 3 \):

\[ 4k + 1 = 0 \]

### Step 4: Solve for \( k \)

Next, we isolate \( k \) by moving \( 1 \) to the other side:

\[ 4k = -1 \]

Now, divide both sides by \( 4 \):

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

### Final Answer

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

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

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