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Formation of a Quadratic Equation From It's Roots

If α, β, γ ar...

Question

If α, β, γ are the zeroes of the polynomial p(x) = 6x³ + 3x²− 5x + 1, find the value of $(\frac{1}{α} + \frac{1}{β} + \frac{1}{γ})$

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Solution

$Given : p (x) = 6 x^{3} + 3 x^{2} - 5 x + 1 = 6 x^{2} - (- 3) x^{2} + (- 5) x - (- 1)$

Comparing the polynomial with $x^{3} - x^{2} (α + β + γ) + x (α β + β γ + γ α) - α β γ$ , we get:
$α β + β γ + γ α = - 5 and α β γ = - 1 ∴ (\frac{1}{α} + \frac{1}{β} + \frac{1}{γ}) = (\frac{β γ + α γ + α β}{α β γ}) = (\frac{- 5}{- 1}) = 5$

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Formation of a Quadratic Equation From It's Roots

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