Question

If one root of the quadratic equation \( x^2 + 2kx + 4 = 0 \) is 2, then the value of \( k \) is:

• A. \( -1 \)
• B. \( -2 \)
• C. \( 2 \)
• D. \( -4 \)

Hint:

To determine an unknown coefficient when a root is given, substitute the root into the quadratic equation and solve for the unknown variable.

Answer 1

The Correct Option is B

Step 1: Use the root substitution method Since \( x = 2 \) is a root, it must satisfy the equation: \[ 2^2 + 2k(2) + 4 = 0 \] Step 2: Solve for \( k \) \[ 4 + 4k + 4 = 0 \] \[ 8 + 4k = 0 \] \[ 4k = -8 \] \[ k = -2 \] Thus, the correct answer is \( -2 \).