If one of the zeros of the quadratic polynomial `(k - 2)x^2 - 2x - (k+5)` is 4, find the value of k

Answer

To find the value of \( k \) given that one of the zeros of the quadratic polynomial \( (k - 2)x^2 - 2x - (k + 5) \) is 4, we can follow these steps:

### Step 1: Substitute the zero into the polynomial
Since 4 is a zero of the polynomial, we substitute \( x = 4 \) into the polynomial equation:
\[ (k - 2)(4^2) - 2(4) - (k + 5) = 0 \]

### Step 2: Simplify the equation
Calculating \( 4^2 \):
\[ (k - 2)(16) - 8 - (k + 5) = 0 \]
Expanding the equation:
\[ 16k - 32 - 8 - k - 5 = 0 \]

### Step 3: Combine like terms
Combine the constants and the \( k \) terms:
\[ 16k - k - 32 - 8 - 5 = 0 \]
This simplifies to:
\[ 15k - 45 = 0 \]

### Step 4: Solve for \( k \)
Now, we can solve for \( k \):
\[ 15k = 45 \]
\[ k = \frac{45}{15} = 3 \]

### Conclusion
The value of \( k \) is \( 3 \).

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