For which value of p will the equation `(p^2-1)x^2+px+q=0` not be a quadratic equation?

Options

A. p=1
B. p=-1
C. Both (i) and (ii)
D. p=0

Answer

To determine the value of \( p \) for which the equation \((p^2 - 1)x^2 + px + q = 0\) is not a quadratic equation, we need to analyze the coefficient of \( x^2 \).

### Step-by-step Solution:

1. **Identify the Coefficient of \( x^2 \)**:
The given equation is \((p^2 - 1)x^2 + px + q = 0\). The coefficient of \( x^2 \) is \( p^2 - 1 \).

2. **Set the Coefficient Equal to Zero**:
For the equation to not be a quadratic equation, the coefficient of \( x^2 \) must be zero. Therefore, we set:
\[ p^2 - 1 = 0 \]

3. **Solve for \( p \)**:
Rearranging the equation gives:
\[ p^2 = 1 \]
Taking the square root of both sides, we find:
\[ p = 1 \quad \text{or} \quad p = -1 \]

4. **Conclusion**:
The values of \( p \) for which the equation is not a quadratic equation are \( p = 1 \) and \( p = -1 \).

### Final Answer:
The values of \( p \) are \( 1 \) and \( -1 \).