Question

If \( x = -1 \) is a common root of both 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:

If a common root is given, substitute it into both equations and solve for unknowns.

Answer 1

The Correct Option is B

Since \( x = -1 \) is a root of both equations, substituting \( x = -1 \):
For \( 2(-1)^2 + 3(-1) + p = 0 \):
\[ 2 - 3 + p = 0 \Rightarrow p = 1 \] For \( q(-1)^2 - q(-1) + 4 = 0 \):
\[ q + q + 4 = 0 \Rightarrow 2q = -4 \Rightarrow q = -2 \] Thus:
\[ p + q = 1 + (-2) = -1 \]