Question

If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \( p(x) = x^2 + 3x - 4 \), then the value of \( \frac{\alpha \beta}{4} \) is:

• A. \( -1 \)
• B. \( 1 \)
• C. \( 4 \)
• D. \( -4 \)

Hint:

For a quadratic equation \( ax^2 + bx + c = 0 \), the roots satisfy: \[ \alpha + \beta = -\frac{b}{a}, \quad \alpha \beta = \frac{c}{a}. \]

Answer 1

The Correct Option is B

From the quadratic equation, the product of the roots is:
\[ \alpha \beta = c/a = \frac{-4}{1} = -4. \] Thus, \[ \frac{\alpha \beta}{4} = \frac{-4}{4} = -1. \]