Question

In the relation between zeroes (roots) and coefficients of \[ ax^{2} + bx + c = 0 \], what is the status of the pairwise product of the roots?

Options

• It equals \( -\dfrac{b}{a} \)

• It equals \( \dfrac{b}{a} \)

• Not applicable

• It equals \( \dfrac{c}{a} \)

Answer 1

For \[ ax^{2} + bx + c = 0 \], only two roots \( \alpha, \beta \) exist, so the pairwise product is Not applicable. Pairwise product \( \alpha\beta + \beta\gamma + \gamma\alpha \) is defined only for the cubic equation \[ ax^{3} + bx^{2} + cx + d = 0 \].