Question

if alpha and beta are the zeros of x square + 7x + 12 then find the value of one upon alpha + one upon beta minus 2 alpha beta

Answer 1

Given

p(x)= x²+7x+12

here,

a= 1, b= 7 and c= 12

we know that,

sum of zeroes= -b/a

$\alpha + \beta = - 7$
_______________(1)
also,

Product of zeroes= c/a

$\alpha \beta = 12$
__________________(2)


now,

$\frac{1}{ \alpha } + \frac{1}{ \beta } - 2 \alpha \beta \\ \\ = \frac{ \alpha + \beta }{ \alpha \beta } - 2 \alpha \beta \\ \\ = \frac{( \alpha + \beta ) - \alpha \beta (2 \beta )}{ \alpha \beta }$
from (1) and (2), we have,

$\frac{ - 7 - 12(24)}{12} \\ \\ = \frac{ -7 - 288}{12} \\ \\ = - \frac{295}{12}$