Question

the roots of the equation ax²+bx+c=0 are α and β .Form the quadratic equation whose roots are α+1/β and β+1/α

Answer 1

Hope this help you..........

Answer 2

Answer:

$\alpha + \beta = - \frac{b}{a} \: and \: \: \alpha \beta = \frac{c}{a}$

Now,

$( \alpha + \frac{1}{ \beta } ) + ( \beta + \frac{1}{ \alpha } ) = ( \alpha + \beta ) + ( \frac{ \alpha + \beta }{ \alpha \beta }) = - \frac{b}{a} - \frac{b}{c} = - b( \frac{c + a}{ac} )$

also

$( \alpha + \frac{1}{ \beta } )( \beta + \frac{1}{ \alpha } ) = \alpha \beta + 1 + 1 + \frac{1}{ \alpha \beta } = 2 + \frac{c}{a} + \frac{a}{c}$

so EQ is,

${x}^{2} + b( \frac{c + a}{ac} )x + 2 + \frac{c}{a} + \frac{a}{c} = 0$