Question

If \(\alpha, \beta\) are the zeros of the polynomial \(P(x) = 3x^2 - x - 4\), then \(\alpha \times \beta =\)

• A. \(-\frac{4}{3}\)
• B. \(\frac{4}{3}\)
• C. \(-\frac{1}{3}\)
• D. \(\frac{1}{3}\)

Hint:

For quadratic equations, use Vieta's formulas: the sum and product of roots are related to the coefficients of the equation.

Answer 1

The Correct Option is C

For a quadratic equation \(ax^2 + bx + c\), the product of the roots \(\alpha\) and \(\beta\) is given by: \[ \alpha \times \beta = \frac{c}{a} \] For \(P(x) = 3x^2 - x - 4\), \(a = 3\), \(b = -1\), and \(c = -4\). Therefore, \[ \alpha \times \beta = \frac{-4}{3} \] Thus, the correct answer is \(-\frac{1}{3}\).