Question

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

Options

• \( \dfrac{c}{a} \)

• \( \dfrac{d}{a} \)

• \( -\dfrac{c}{a} \)

• \( -\dfrac{d}{a} \)

Answer 1

For \[ ax^{3} + bx^{2} + cx + d = 0: \quad \alpha\beta + \beta\gamma + \gamma\alpha = \frac{c}{a} \]. The sum of the pairwise products of the roots equals the coefficient of \( x \) divided by the leading coefficient \( a \).