Question

if alpha,beta and gama are zeros of polynomial 6x3+3x2-5x+1 then find value of alpha di power-1 + beta di power- 1 + gama di power-1

Answer 1

HELLO DEAR,


Given that:-


we have to find,

α^-1 + β^-1 + γ^-1


⇒1/α + 1/β + 1/γ


⇒(βγ + αγ + αβ)/αβγ-------------(1)




Now,



From the GIVEN Equation:-


6x³ + 3x² - 5x + 1 = 0


Where,


a = 6

b = 3

c = (-5)

d = 1



we know that:-

α + β + γ = -b/a = -3/6 = -1/2

αβγ = -d/a = -1/6

αβ + βγ + αγ = c/a = -5/6



Put the values in -----(1)


We get,

⇒(βγ + αγ + αβ)/αβγ


⇒ (-5/6) / (-1/6)


⇒30/6

⇒5




I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

hope it's clear!
thank you