Question

The ratio of the sum and product of the roots of the equation $7x^2-12x+18=0$
(a) 7 : 12
(b) 7 : 18
(c) 2 : 3
(d) 3 : 2

Answer 1

(c) 2 : 3

$$\begin{gathered} \text{Given:} \\ \text{7}{x}^2-12x+18=0 \\ \therefore \alpha +\beta =\frac{12}{7}\text{and}\alpha \beta =\frac{18}{7},\mathrm{where}\alpha \mathrm{and}\beta \mathrm{are}\mathrm{the}\mathrm{roots}\mathrm{of}\mathrm{the}\mathrm{equation} \\ \therefore \text{Ratio of the sum and product of the roots =}\frac{12}{7}:\frac{18}{7} \\ =12:18 \\ =2:3 \end{gathered}$$