roots

find all roots of

x⁴+x³+x²+x+1=0

including complex roots.

4 Answers

NO POSITIVE REAL ROOTS.................

MAX 4 NEGATIVE REAL ROOTS. MINIMUM ZERO COMPLEX ROOT......... MAXIMUM 4 COMPLEX ROOTS...........

Dividing both sides by x² , we get

x^{2}\ +\ x\ +\ 1\ +\ \frac{1}{x}\ +\ \frac{1}{x^{2}}\ =\ 0

Now\ put\ (x\ +\ \frac{1}{x})\ =\ y

We \ get\ (y^{2}\ +\ y\ -\ 1 ) \ =\ 0

106

Asish Mahapatra ·2010-12-08 17:43:04

alternatively using formula for GP,

it is x⁵-1x-1 = 0

i.e. x⁵-1 = 0 and x â‰ 1

hence it is fifth roots of unity excluding 1

all the roots are complex ,,well done tush ,,,,,, its the correct method

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