Question

find the quadratic equation whose roots are the reciprocals of the roots of x^2 + 4x - 10 = 0

Answer 1

$let \: the \: roots \: of \: given \: eq \: be \: \alpha \: and \: \beta \\ so \: \\ \: \: \: \: \: \alpha + \beta = - 4 \\ \: \: \: \: \: \alpha \beta = - 10 \\ the \: eq \: with \: roots \: \frac{1}{ \alpha } and \: \frac{1}{ \beta } is \\ \: {x}^{2} - ( \frac{1}{ \alpha } + \frac{1}{ \beta } )x + \frac{1}{ \alpha \beta } = 0 \\ {x}^{2} - ( \frac{ \alpha + \beta }{ \alpha \beta } )x + \frac{1}{ \alpha \beta } = 0 \\ {x}^{2} - ( \frac{ - 4}{ - 10} )x + \frac{1}{ - 10} = 0 \\ {x}^{2} - \frac{2}{5} x - \frac{1}{10} = 0 \\ multiply \: whole \: eq \: with \: 10 \\ 10 {x}^{2} - 4x - 1 = 0$
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