The ratio of the sum and product of the roots of the equation
Question:

The ratio of the sum and product of the roots of the equation $7 x^{2}-12 x+18=0$

(a) 7 : 12
(b) 7 : 18
(c) 2 : 3
(d) 3 : 2

Solution:

(c) 2 : 3

Given:

$7 x^{2}-12 x+18=0$

$\therefore \alpha+\beta=\frac{12}{7}$ and $\alpha \beta=\frac{18}{7}$, where $\alpha$ and $\beta$ are the roots of the equation

$\therefore$ Ratio of the sum and product of the roots $=\frac{12}{7}: \frac{18}{7}$

$=12: 18$

$=2: 3$