One root of the equation `x^(2) = px +q` is reciprocal of the other and `p!=pm1`. What is the value of q ?

Options

A. ` q=-1`
B. ` q=-1`
C. ` q=0`
D. ` q= 1/2`

Explanation

To solve the problem, we start with the given quadratic equation:

\[ x^2 = px + q \]

We can rearrange this equation into standard form:

\[ x^2 - px - q = 0 \]

Let the roots of this equation be \( \alpha \) and \( \frac{1}{\alpha} \) (since one root is the reciprocal of the other).

### Step 1: Use the relationship of the roots
From Vieta's formulas, we know that:
1. The sum of the roots \( \alpha + \frac{1}{\alpha} = p \)
2. The product of the roots \( \alpha \cdot \frac{1}{\alpha} = 1 = -\frac{q}{1} \)

### Step 2: Find the product of the roots
From the product of the roots, we have:

\[ \alpha \cdot \frac{1}{\alpha} = 1 \]

This implies:

\[ 1 = -\frac{q}{1} \]

### Step 3: Solve for \( q \)
Rearranging the equation gives:

\[ q = -1 \]

Thus, the value of \( q \) is:

\[ \boxed{-1} \]