Question

If one root of the equation \( x^2 - 4x + k = 0 \) is 6, then the value of \( k \) will be:

• A. -12
• B. -6
• C. 6
• D. 12

Hint:

To find the value of a constant in a quadratic equation, substitute one of the given roots into the equation and solve for the constant.

Answer 1

The Correct Option is B

The given equation is: \[ x^2 - 4x + k = 0 \] We know that one root of this quadratic equation is \( x = 6 \). By substituting \( x = 6 \) into the equation, we get: \[ 6^2 - 4(6) + k = 0 \] Simplifying: \[ 36 - 24 + k = 0 \] \[ 12 + k = 0 \] \[ k = -6 \]
Step 1: Conclusion.
Thus, the value of \( k \) is \( -6 \).