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 general form of a quadratic equation**:
A quadratic equation is generally in the form \( ax^2 + bx + c = 0 \), where \( a \neq 0 \). Here, \( a \) is the coefficient of \( x^2 \).

2. **Set the coefficient of \( x^2 \) to zero**:
For the given equation \((p^2 - 1)x^2 + px + q = 0\), the coefficient of \( x^2 \) is \( p^2 - 1 \). For the equation to not be quadratic, we need:
\[ p^2 - 1 = 0 \]

3. **Solve for \( p \)**:
Rearranging the equation gives:
\[ p^2 = 1 \]
Taking the square root of both sides, we find:
\[ p = \pm 1 \]
Thus, the values of \( p \) that make the equation not quadratic are \( p = 1 \) and \( p = -1 \).

4. **Conclusion**:
Therefore, the values of \( p \) for which the equation \((p^2 - 1)x^2 + px + q = 0\) is not a quadratic equation are \( p = 1 \) and \( p = -1 \).