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When 3 – √5 is a root, 3 + √5 is the other root. S.o.r. = (3 – √5) + (3 + √5) = 6 = (3 – √5) (3 + √5) = 32 - (√5)2 = 9 - 5 = 4 The equation is x2 – 6x + 4 = 0 Now x4 – 7x3 + 8x2 + 8x – 8 = (x2 – 6x + 4) (x2 + px – 2) Equating co-eff of x 12 + 4p = 8 4p = 8 – 12 = -4 So the other factor is x2 – x – 2 Now solving x2 – x – 2 = 0 Read more on Sarthaks.com - https://www.sarthaks.com/907340/solve-for-x-2-7x-3-8x-2-8x-8-0-given-3-5-is-a-root
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