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 polynomial \( ax^2 + bx + c \), the product of the zeroes is \( \alpha \beta = \frac{c}{a} \).

Answer 1

The Correct Option is A

Step 1: The product of the zeroes of the quadratic polynomial \( p(x) = x^2 + 3x - 4 \) is given by \( \alpha \beta = \frac{c}{a} \), where \( a = 1 \) and \( c = -4 \). Step 2: Thus, the product of the zeroes is: \[ \alpha \beta = \frac{-4}{1} = -4 \] Step 3: Now, we find the value of \( \frac{\alpha \beta}{4} \): \[ \frac{\alpha \beta}{4} = \frac{-4}{4} = -1 \] Thus, the correct answer is \( \frac{\alpha \beta}{4} = -1 \), which corresponds to option (A).