Question

find the quadratic equation whose roots are reciprocal of the roots of the equation 3x2-20x+17=0

Answer 1

$3 {x }^{2} - 20x + 17 = 0 \\ let \: \alpha \: \beta \: be\: roots \\ \alpha + \beta = \frac{20}{3} \\ \alpha \beta = \frac{17}{3} \\ quardic \: equation \: has \: root \: \frac{1}{ \alpha } and\frac{1}{ \beta } \\ {x}^{2} - ( \frac{1}{ \alpha } + \frac{1}{ \beta } )x + \alpha \beta \\ = {x}^{2} - ( \frac{ \alpha + \beta }{ \alpha \beta } )x + \alpha \beta \\ = {x}^{2} - ( \frac{ \frac{20}{3} }{ \frac{17}{3} } )x + \frac{17}{3} \\ = {x }^{2} - \frac{20}{17} x + \frac{17}{3} \\ = \frac{51 {x}^{2} - 60x + 289 }{51} \\ hence \: eq. \: is \: 51 {x}^{2} - 60x + 289$