Question

If \( x = -1 \) is a common root of the equations \( 2x^2 + 3x + p = 0 \) and \( qx^2 - qx + 4 = 0 \), then the value of \( p + q \) is:

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

Hint:

A common root means the given value satisfies both equations. Solve separately and then sum the results.

Answer 1

The Correct Option is B

Step 1: Substitute \( x = -1 \) into the first equation \[ 2(-1)^2 + 3(-1) + p = 0 \] \[ 2 - 3 + p = 0 \] \[ p = 1 \] Step 2: Substitute \( x = -1 \) into the second equation \[ q(-1)^2 - q(-1) + 4 = 0 \] \[ q + q + 4 = 0 \] \[ 2q + 4 = 0 \] \[ 2q = -4 \] \[ q = -2 \] Step 3: Compute \( p + q \) \[ p + q = 1 + (-2) = -1 \] Thus, the correct answer is \( -1 \).