Question

If one root of the equation \( x^2 - kx - 8 = 0 \) is 2, then the value of \( k \) will be:

• A. 8
• B. -2
• C. 2
• D. 4

Hint:

Always substitute the root directly into the equation to find unknown coefficients. Be careful with negative signs.

Answer 1

The Correct Option is A

Step 1: Substitute the known root in the equation.
Given that \( x = 2 \) is a root of \( x^2 - kx - 8 = 0 \), substitute \( x = 2 \): \[ (2)^2 - k(2) - 8 = 0 \]
Step 2: Simplify.
\[ 4 - 2k - 8 = 0 \] \[ -2k - 4 = 0 \] \[ -2k = 4 \] \[ k = -2 \] Wait—check the signs: The given equation is \( x^2 - kx - 8 = 0 \). If \( x = 2 \): \[ 4 - 2k - 8 = 0 \Rightarrow -2k = 4 \Rightarrow k = -2 \] Hence, the correct answer is \( -2 \).
Step 3: Conclusion.
The value of \( k \) is \( \boxed{-2} \).