How would you find the exact roots of y = x 3 </msup> + x 2

hawwend8u 2022-05-23 Answered
How would you find the exact roots of y = x 3 + x 2 2 x 1?
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Answers (1)

Brooks Butler
Answered 2022-05-24 Author has 9 answers
Let p ( x ) = x 3 + x 2 2 x 1, we have
p ( t + t 1 ) = t 3 + t 2 + t + 1 + t 1 + t 2 + t 3 = t 7 1 t 3 ( t 1 )
The RHS has roots of the form t = e ± 2 k π 7 i ( coming from the t 7 1 factor in numerator ) for k=1,2,3. So p(x) has roots of the form
e 2 k π 7 i + e 2 k π 7 i = 2 cos ( 2 k π 7 )
for k=1,2,3
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