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Manager  S
Joined: 18 Jul 2019
Posts: 54
If the sum of the reciprocals of the roots of the equation ax^2+bx+c=0  [#permalink]

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4 00:00

Difficulty:   65% (hard)

Question Stats: 35% (01:55) correct 65% (02:07) wrong based on 17 sessions

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If the sum of the reciprocals of the roots of the equation $$ax^2 + bx + c = 0$$ is $$11/28$$ and the product of the roots of the equation $$cx^2 + bx + a = 0$$ is $$1/28$$, find the sum of the roots of the equation $$bx^2 +ax+ c = 0$$

(A) 28/11
(B) -28/11
(C) 1/11
(D) -1/11
(E) -1/28
Math Expert V
Joined: 02 Aug 2009
Posts: 8305
Re: If the sum of the reciprocals of the roots of the equation ax^2+bx+c=0  [#permalink]

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CaptainLevi wrote:
If the sum of the reciprocals of the roots of the equation $$ax^2 + bx + c = 0$$ is $$11/28$$ and the product of the roots of the equation $$cx^2 + bx + a = 0$$ is $$1/28$$, find the sum of the roots of the equation $$bx^2 +ax+ c = 0$$

(A) 28/11
(B) -28/11
(C) 1/11
(D) -1/11
(E) -1/28

The sum of the reciprocals of the roots of the equation $$ax^2 + bx + c = 0$$ is $$11/28$$
If x and y are roots, the reciprocal and their sum = $$\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}=\frac{Sum}{Product}=\frac{\frac{-b}{a}}{\frac{c}{a}}=\frac{-b}{c}=\frac{11}{28}$$..

the product of the roots of the equation $$cx^2 + bx + a = 0$$ is $$1/28$$ ------ $$\frac{a}{c}=\frac{1}{28}$$,

find the sum of the roots of the equation $$bx^2 +ax+ c = 0$$ ----$$\frac{-a}{b}=\frac{a}{c}*\frac{c}{-b}=\frac{1}{28}*\frac{28}{11}=\frac{1}{11}$$

C
_________________ Re: If the sum of the reciprocals of the roots of the equation ax^2+bx+c=0   [#permalink] 28 Nov 2019, 05:56
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# If the sum of the reciprocals of the roots of the equation ax^2+bx+c=0  