Question

If alpha and beta are the zeros of 4x2 +3x +7 then find the value of 1/alpha + 1/beta +2alphabeta

Answer 1

$\alpha \beta = product \: of \: roots$

= c/ a = 7/4

and

$\alpha + \beta = sum \: of \: roots$

= -b/a = -3/4

so , 1/ alpha + 1/beta + 2alphabeta

= (alpha+ beta)/alphabeta + 2alphabeta

= (-3/4)/7/4 +2.(7/4)

= -3/7+7/2

= -6+49/14

= 43/14

hope it helps ^_^