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The ratio of the sum of the roots of $x^{2} - 9 x + 18 = 0$ to the product of the roots is-

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1 : 2

2 : 1

- 1 : 2

- 2 : 1

answer is A.

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Detailed Solution

Given that, the quadratic equation is

x^{2} - 9 x + 18 = 0

.
We need to find the ratio of the sum of the roots to the product of the roots.
We know that if an equation is of the form

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

, then the sum of roots

= \frac{- b}{a}

and the product of roots

= \frac{c}{a}

.
Here,
Sum of roots

= - (- 9)

.
Product of the roots

= 18

.
Therefore,

\frac{Sum of roots}{Product of roots} = \frac{9}{18} = \frac{1}{2}

Therefore, the ratio of the sum of roots to the product of roots is

1 : 2

.
Hence, option 1 is correct.

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