What is the value of k, if one of the zeroes of the quadratic polynomial `(k - 2)x^2 - 2x - 5` is-1?

Options

A. 5
B. 3
C. `-5`
D. 0

Answer

To find the value of \( k \) such that one of the zeroes of the quadratic polynomial \( (k - 2)x^2 - 2x - 5 \) is -1, we can follow these steps:

### Step 1: Substitute the zero into the polynomial
We know that if -1 is a zero of the polynomial, then substituting \( x = -1 \) into the polynomial should yield 0.

The polynomial is:
\[ (k - 2)(-1)^2 - 2(-1) - 5 \]

### Step 2: Simplify the expression
Now, simplify the expression:
\[ (k - 2)(1) + 2 - 5 = 0 \]
This simplifies to:
\[ k - 2 + 2 - 5 = 0 \]

### Step 3: Combine like terms
Combine the constants:
\[ k - 5 = 0 \]

### Step 4: Solve for \( k \)
Now, isolate \( k \):
\[ k = 5 \]

Thus, the value of \( k \) is \( 5 \).

### Final Answer:
\[ \boxed{5} \]