Question

if alpha,beta,gamma are zeroes of polynomial 6x³+3x²-5x+1, then find the value of alpha raised to -1 + beta raised to -1 + gamma raised to -1

Answer 1

From the ques,

Sum of zeroes: 

(α+β+γ) = (-b/a) = -(3/1) = -3/6 = -1/2

Sum of products of zeroes taken at two time:

(αβ+βγ+γα) = (c/a) = (-5/1) = -5/6

Product of zeroes:

(αβγ) = (-d/a) = -(1/1) = -1/6
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To find: 1/α + 1/β + 1/γ

= 1/α + 1/β + 1/γ

= (βγ + γα + αβ) / αβγ

= (-5/6)/(-1/6)

= 5
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