Question

For the quadratic equation \[ ax^{2} + bx + c = 0 \] with roots \[ \alpha, \beta \], which expression gives the product of the roots \( \alpha\beta \)?

Options

• \( -\dfrac{b}{a} \)

• \( \dfrac{c}{a} \)

• \( -\dfrac{c}{a} \)

• \( \dfrac{b}{a} \)

Answer 1

For \[ ax^{2} + bx + c = 0 \], the relation between zeroes and coefficients states that \[ \alpha\beta = \frac{c}{a} \]. The product of the roots equals the constant term divided by the coefficient of \( x^{2} \), with no sign change.