Question

if alpha,beta,gamma are the zeros of polynomial 6x cube+3xsquare-5x+1 find valu of alpha,beta,gamma

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,

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Answer 2

Given α,β & ɣ are the roots of the polynomials 6x3 + 3x2 - 5x + 1 = 0 then

α+β+ɣ  = -3/6 = -1/2

αβ+βɣ+αɣ = -5/6

αβɣ = -1/6

α-1 + β-1 + ɣ-1 = 1/α + 1/β + 1/ɣ = (αβ+βɣ+αɣ) / αβɣ = -5/6 / -1/6 = 5

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