Question

If \( \alpha \) and \( \beta \) are the zeros 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:

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

Answer 1

The Correct Option is A

Using Vieta’s formulas:
\[ \alpha + \beta = -\frac{-3}{1} = 3. \] \[ \frac{4}{3} (\alpha + \beta) = \frac{4}{3} \times 3 = 4. \]