Question

For the cubic equation \[ ax^{3} + bx^{2} + cx + d = 0 \] with roots \[ \alpha, \beta, \gamma \], the product of the roots \( \alpha\beta\gamma \) equals:

Options

• \( \dfrac{c}{a} \)

• \( -\dfrac{d}{a} \)

• \( -\dfrac{b}{a} \)

• \( \dfrac{d}{a} \)

Answer 1

For \[ ax^{3} + bx^{2} + cx + d = 0: \quad \alpha\beta\gamma = -\frac{d}{a} \]. Note that the product of the roots of a cubic carries a negative sign, unlike the quadratic case where \( \alpha\beta = \frac{c}{a} \).