Question

The ratio of the sum and product of the roots of the quadratic equation \(7x^2-12x+18=0\) is

• A. 7:12
• B. 7:18
• C. 3:2
• D. 2:3

Answer 1

The Correct Option is D

1. Identify coefficients:

In the equation \(ax^2 + bx + c = 0\), we have \(a = 7\), \(b = -12\), and \(c = 18\).

2. Sum of roots:

Sum = \(\frac{-b}{a} = \frac{-(-12)}{7} = \frac{12}{7}\)

3. Product of roots:

Product = \(\frac{c}{a} = \frac{18}{7}\)

4. Calculate the ratio:

Ratio = (Sum) : (Product) = \(\frac{12}{7} : \frac{18}{7} = 12 : 18 = 2 : 3\)