Question

If \( x = 2 \) is a common root of the equations \( 2x^2 + 2x + p = 0 \) and \( qx + qx + 18 = 0 \), then the value of \( (q - p) \) is:

• A. \( -4 \)
• B. \( -3 \)
• C. \( 9 \)
• D. \( 4 \)

Hint:

If a given value is a root of a polynomial equation, substitute it in the equation to solve for unknown parameters.

Answer 1

The Correct Option is C

Since \( x = 2 \) is a root of the first equation: \[ 2(2)^2 + 2(2) + p = 0. \] \[ 2(4) + 4 + p = 0. \] \[ 8 + 4 + p = 0. \] \[ p = - \] For the second equation: \[ q(2) + q(2) + 18 = 0. \] \[ 2q + 2q + 18 = 0. \] \[ 4q + 18 = 0. \] \[ q = -\frac{18}{4} = -4.5. \] Now, finding \( q - p \): \[ q - p = (-4.5) - (-12) = -4.5 + 12 = 7.5. \]