Question

Find the sum of the reciprocal of the root of the equation 2 − 9 − 20 = 0​

Answer 1

Answer:

Correct Questions.

$\sf \: 2 {x}^{2} - 9x - 20 = 0$

here

a= 2, b=-9 , c= -20

$\sf \: \frac{1 }{ \alpha } + \frac{1}{ \beta }$

$\sf \: = \frac{ \alpha + \beta }{ \alpha \beta }$

$\sf \: Sum \: of \: roots = ( \alpha + \beta ) = - \frac{b}{a} = - \frac{ - 9}{2}$

$\sf \: Sum \: of \: roots =\frac{ 9}{2}$

$\sf \: Product \: of \: roots = \alpha \beta = \frac{c}{a} = - \frac{20}{2} = - 10$

$\sf \: = \frac{ \alpha + \beta }{ \alpha \beta } = \frac{9}{2} \div( -10) = -\frac{9}{20}$