Question

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

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

To find the unknown in a quadratic equation when one root is given, substitute the value of \( x \) directly into the equation and solve for the unknown.

Answer 1

The Correct Option is C

Step 1: Substitute the given root.
The given equation is \( x^2 + 2x - p = 0 \). One root is \( x = -2 \). Substituting it in the equation: \[ (-2)^2 + 2(-2) - p = 0 \]
Step 2: Simplify.
\[ 4 - 4 - p = 0 \Rightarrow -p = 0 \Rightarrow p = 0 \] Wait — let’s check carefully again: \( 4 - 4 - p = 0 \Rightarrow p = 0 \). Actually, let’s verify: both terms cancel, leaving \( -p = 0 \). So, \( p = 0 \).
Step 3: Final answer.
\[ p = 0 \]