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

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7: 12

7: 18

3: 2

2: 3

answer is D.

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Detailed Solution

Given quadratic equation is,

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

.
The standard form of a quadratic equation is

a x^{2} + bx + c = 0,

where

a, b c

are real numbers and

a \neq 0

.
And,
The sum of the roots is given by

- \frac{b}{a}

and product of the roots is given by

\frac{c}{a}

.
After comparing

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

with the standard form, we get,

a = 7, b = - 12, c = 18

Then,
Sum of the roots

= - \frac{b}{a}

= - \frac{(- 12)}{7}

= \frac{12}{7}

Product of the roots =

\frac{c}{a} = \frac{18}{7}

.
The ratio of the sum and product of the roots of the equation =

- \frac{b}{a} ∶ \frac{c}{a}

= \frac{12}{7} ∶ \frac{18}{7}

= 2 ∶ 3

∴

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

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

is 2:3.
Hence, the correct option is 4.

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