Question

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

Answer 1

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☆ ANSWER:-

▪︎ Given Quadratic Equation:-

$\tt\leadsto7 {x}^{2} - 12x + 18 = 0$

▪︎ To Find:-

• The ratio of Sum and Product of the zeroes.

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▪︎ Concepts Used:-

$\sf\leadsto Sum\:Of\:Zeroes = \frac{-b}{a} \\ \\ \sf\leadsto Product\:Of\:Zeroes = \frac{c}{a}$

Where,

• a = Coefficient of x²

• -b = -Coefficient of x.

• c = Constant Term.

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▪︎ Now,

$\tt\mapsto Sum\:Of\:Zeroes = \frac{-b}{a} \\ \\ \tt\mapsto Sum\:Of\:Zeroes = \frac{-(-12)}{7} \\ \\ \tt\mapsto Sum\:Of\:Zeroes = \frac{12}{7}$

And,

$\tt \mapsto Product\:Of\:Zeroes = \frac{c}{a} \\ \\ \tt\mapsto Product\:Of\:Zeroes = \frac{18}{7}$

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▪︎ Therefore,

$\sf \mapsto \frac{Sum\:Of\:Zeroes}{Product\:Of\:Zeroes} = \frac{12/ \cancel{7}}{18/ \cancel{7}} \\ \\ \sf \mapsto \frac{Sum\:Of\:Zeroes}{Product\:Of\:Zeroes} = \cancel\frac{12}{18} \\ \\ \sf \mapsto \frac{Sum\:Of\:Zeroes}{Product\:Of\:Zeroes} = \frac{2}{3} \\ \\ \sf \mapsto Sum\:Of\:Zeroes:Product\:Of\:Zeroes =2:3$

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$\therefore$ The ratio of sum and product of the zeroes = 2:3.

So the final answer is Option C:- 2:3

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