Question

If one root of the quadratic equation \(2x^2 - 7x - p = 0\) is 2 then the value of p is

• A. 4
• B. -4
• C. -6
• D. 6

Hint:

This is a standard problem type. Whenever you are given a root and an unknown coefficient, the first step is always to substitute the root's value into the equation.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
If a number is a root (or zero) of an equation, it means that substituting this number for the variable will make the equation true.

Step 2: Key Formula or Approach:
Substitute the value of the given root, \(x = 2\), into the quadratic equation and solve for the unknown parameter, \(p\).

Step 3: Detailed Explanation:
The given equation is \(2x^2 - 7x - p = 0\).
We are given that one root is \(x = 2\).
Substitute \(x = 2\) into the equation:
\[ 2(2)^2 - 7(2) - p = 0 \] \[ 2(4) - 14 - p = 0 \] \[ 8 - 14 - p = 0 \] \[ -6 - p = 0 \] Now, solve for \(p\):
\[ p = -6 \]

Step 4: Final Answer:
The value of p is -6.