Why does the mariner call albatross 'CHRISTIAN SOUL'???
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In The Rime of the Ancient Mariner, the albatross is called the Christian soul. It was hailed in God's name because it appeared out of nowhere. It seemed like a saviour to the mariners. After the arrival of the albatross, the icebergs started to cracking, making way for the ship to move forward.
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Explanation:
f(x) = kx³ – 8x² + 5
Roots are α – β , α & α +β
Sum of roots = – (-8)/k
Sum of roots = α – β + α + α +β = 3α
= 3α = 8/k
= k = 8/3α
or we can solve as below
f(x) = (x – (α – β)(x – α)(x – (α +β))
= (x – α)(x² – x(α+β + α – β) + (α² – β²))
= (x – α)(x² – 2xα + (α² – β²))
= x³ – 2x²α + x(α² – β²) – αx² +2α²x – α³ + αβ²
= x³ – 3αx² + x(3α² – β²) + αβ² – α³
= kx³ – 3αkx² + xk(3α² – β²) + k(αβ² – α³)
comparing with
kx³ – 8x² + 5
k(3α² – β²) = 0 => 3α² = β²
k(αβ² – α³) = 5
=k(3α³ – α³) = 5
= k2α³ = 5
3αk = 8 => k = 8/3α
(8/3α)2α³ = 5
=> α² = 15/16
=> α = √15 / 4
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