Question

if alpha and beta are the zeroes of quadratic polynomial x^2-33x +7 find a quadratic polynomial whose zeroes are 1/alpha and 1/beta​

Answer 1

if

$\alpha \: and \: \beta$

are the roots of equation

${x}^{2} - 33x + 7$

then ,

$\alpha + \beta =$

- ( co efficient of x ) / co efficient of x² = - (-33) / 1 = 33

and

$\alpha \beta =$

constant / co efficient of x² = 7 / 1 = 7

SO ,

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

=> Sum of new roots ,

$\frac{( \: \alpha + \beta \: )}{ \alpha \beta } = \frac{33}{7}$

=> Product of new roots =

$\frac{1}{ \alpha } \times \frac{1 }{ \beta } = \frac{1}{ \alpha \beta } = \frac{1}{7}$

SO , new equation with roots ,

$\frac{1}{ \alpha } \: \: and \: \: \frac{1}{ \beta }$

is ,

=> x² - ( sum of new roots ) x + product of new roots

=>${x}^{2} + \frac{33}{7} x + \frac{1}{7}$