Question

If one root of the 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:

When one root of a quadratic equation is given, always substitute it into the equation to find the unknown constant directly.

Answer 1

The Correct Option is B

Step 1: Given information.
The quadratic equation is: \[ x^2 + 2x - p = 0 \] and one root is given as $x = -2$.

Step 2: Substitute the value of the root in the equation.
Substitute $x = -2$: \[ (-2)^2 + 2(-2) - p = 0 \] \[ 4 - 4 - p = 0 \]
Step 3: Simplify the equation.
\[ 0 - p = 0 \] \[ p = 0 \]
Step 4: Verification.
Wait — rechecking Step 2 carefully: \[ (-2)^2 + 2(-2) - p = 0 \Rightarrow 4 - 4 - p = 0 \] This simplifies to: \[ -p = 0 \Rightarrow p = 0 \] Hence, the value of \( p \) is indeed \( 0 \).
Final Answer
Final Answer: \[ \boxed{p = 0} \]