Question

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

Options

• \( \dfrac{b}{a} \)

• \( \dfrac{c}{a} \)

• \( -\dfrac{d}{a} \)

• \( -\dfrac{b}{a} \)

Answer 1

For \[ ax^{3} + bx^{2} + cx + d = 0: \quad \alpha + \beta + \gamma = -\frac{b}{a} \]. As in the quadratic case, the sum of the roots is the negative of the coefficient of \( x^{2} \) divided by the leading coefficient \( a \).