Question

.. Find the algebraic equation whose roots are the reciprocals of the roots of x^3+3x^2-7x+6=0
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Answer 1

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• Find the algebraic equation whose roots are the reciprocals of the roots of x^3+3x^2-7x+6=0

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The given equation is

$\bf \longmapsto \: \bf \: {x}^{3} + {3x}^{2} - 7x + 6 = 0$

To get the roots, Reciprocal of the given equation, put

$\boxed{ \pink{\bf :\implies \: x \: = \: \dfrac{1}{y} }}$

we get,

$\bf \longmapsto \: \bf \:\dfrac{1}{ {y}^{3} } + \dfrac{3}{ {y}^{2} } - \dfrac{7}{y} + 6 = 0$

$\bf \longmapsto \: \bf \:1 + 3y - {7y}^{2} + 6 {y}^{3} = 0$

$\boxed{ \pink{\bf :\implies\: {6y}^{3} - {7y}^{2} + 3y + 1 = 0 }}$