Question

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

• A. 4
• B. 3
• C. -3
• D. 1

Hint:

The sum of the zeroes of a quadratic polynomial can be found as \( -\frac{b}{a} \).

Answer 1

The Correct Option is B

The sum of the zeroes \( \alpha + \beta \) of the quadratic polynomial \( p(x) = x^2 - 3x - 4 \) is given by \( \alpha + \beta = -\frac{b}{a} \), where \( a = 1 \) and \( b = -3 \). Thus: \[ \alpha + \beta = -\frac{-3}{1} = 3. \] Now, we calculate \( \frac{4}{3}(\alpha + \beta) \): \[ \frac{4}{3} \times 3 = 4. \] Thus, the correct answer is \( \boxed{4} \).