Question

if a,b and c are the zeroes of polynomial 6x cube + 3x square - 5x+1 then find the value of a°-1 +b°-1 +c°-1​

Answer 1

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

⇒

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