Question

If k is ratio of zeroes of the polynomial 4x^(2)-5x-3 then the value of (k+(1)/(k))^(-2) is

Answer 1

Answer:

$4{x}^{2} - 5x - 3 = 0$

let zeros are

$\alpha \: and \: \beta$

so

$\frac{ \alpha }{ \beta } = k \: \: and \: \alpha + \beta = \frac{5}{4} and \: \alpha \beta = \frac{ - 3}{4}$

$\frac{1}{k} = \frac{ \beta }{ \alpha }$

so

$(k + \frac{1}{k} ) {}^{ - 2} = ( \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } ) {}^{ - 2} =$

$( \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } ) {}^{ - 2} = ( \frac{ \alpha \beta }{( \alpha + \beta ) {}^{2} - 2 \alpha \beta } ) {}^{2} =$

$( \frac{ \frac{ - 3}{4} }{ \frac{5}{4} {}^{2} + \frac{6}{4} } ) {}^{2} = ( \frac{ - 3}{4} \times \frac{16}{49} ) {}^{2} = ( - \frac{ 12}{49} ) {}^{2}$

$= \frac{144}{2401} \: \: \: ans.$

Mark BRAINLIEST if you think it is helpful. thanks