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If , , be Zero of polynomial 6x^3 +3x^2 -5x +1 then find th

Question

If $α, β, γ$ be Zero of polynomial $6 x^{3} + 3 x^{2} - 5 x + 1$ then find the value of $α^{- 1}, β^{- 1}, γ^{- 1}$

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Elijah Discussed

α, β, γ

be Zero of polynomial

6 x^{3} + 3 x^{2} - 5 x + 1

then find the value of

α^{- 1}, β^{- 1}, γ^{- 1}

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

P (x) = 6 x^{3} + 3 x^{2} - 5 x + 1

a = 6, b = 3, c = - 5, d = 1

∵ α, β

and

γ

are zeros of the polynomial

p (x)

∴ α + β + γ = \frac{- b}{a} = \frac{- 3}{6} = \frac{- 1}{2}

α β + α γ + β γ = \frac{c}{a} = \frac{- 5}{6}

and

α β γ = \frac{- d}{a} = \frac{- 1}{6}

Now

α^{- 1} + β^{- 1} + γ^{- 1} = \frac{1}{α} = \frac{1}{β} = \frac{1}{γ} = \frac{β γ + α γ + α β}{β γ} = \frac{- 5/6}{- 1/6} = 5

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Question Text	If $α, β, γ$ be Zero of polynomial $6 x^{3} + 3 x^{2} - 5 x + 1$ then find the value of $α^{- 1}, β^{- 1}, γ^{- 1}$
Answer Type	Text solution:1
Upvotes	150