If one of the zeroes of the quadratic polynomial `x^2+3x+k` is 2, then find the value of k:

Options

A. 10
B. -10
C. -8
D. 8

Answer

To find the value of \( k \) in the quadratic polynomial \( x^2 + 3x + k \) given that one of its zeroes is 2, we can follow these steps:

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

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

### Step 2: Calculate the left side
Now, we calculate \( 2^2 \) and \( 3(2) \):

\[ 4 + 6 + k = 0 \]

### Step 3: Combine the constants
Combine the constants on the left side:

\[ 10 + k = 0 \]

### Step 4: Solve for \( k \)
To find \( k \), we can isolate it by subtracting 10 from both sides:

\[ k = -10 \]

### Final Answer
The value of \( k \) is \( -10 \).

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