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If the sum of the reciprocals of the roots of the equation ax^2+bx+c=0

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

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New post 24 Nov 2019, 23:21
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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
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Re: If the sum of the reciprocals of the roots of the equation ax^2+bx+c=0  [#permalink]

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New post 28 Nov 2019, 05:56
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 \(bx^2 +ax+ c = 0\) ----\(\frac{-a}{b}=\frac{a}{c}*\frac{c}{-b}=\frac{1}{28}*\frac{28}{11}=\frac{1}{11}\)

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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

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