Solve the equation 8x^3−38x^2+57x−27=0

luxlivinglm

luxlivinglm

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2022-08-29

Solve the equation 8 x 3 38 x 2 + 57 x 27 = 0

Answer & Explanation

microgrupuv

microgrupuv

Beginner2022-08-30Added 6 answers

Let the roots be a , a r , a r 2
So using Vieta's formula a + a r + a r 2 = 38 8 a ( 1 + r + r 2 ) = 19 4
and a ( a r ) + a r ( a r 2 ) + a r 2 ( a ) = 57 8 a 2 r ( 1 + r 2 + r ) = 57 8
Divide to get a r = 57 8 19 4 = 3 2 as a ( 1 + r + r 2 ) 0
Put a = 3 2 r in the first equation

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