Expressing the roots of \(\displaystyle{y}^{{5}}+{11}{y}^{{4}}-{77}{y}^{{3}}+{132}{y}^{{2}}-{77}{y}+{11}={0}\) terms of

Sanai Huerta

Sanai Huerta

Answered question

2022-04-04

Expressing the roots of y5+11y477y3+132y277y+11=0 terms of of ζ11?

Answer & Explanation

paganizaxpo3

paganizaxpo3

Beginner2022-04-05Added 8 answers

If t7=1 and t1, then x=1+2t+t1 is a root of x3+7x2+7x7=0 but the six primitive 7th roots come in conjugate pairs giving the three roots of the cubic in x.
If t11=1 and t1, then z=t+t12 is a root of z5+11z4+44z3+77z2+55z+11=0 but the ten primitive 11th roots come in conjugate pairs giving the five roots of the quintic in z and the five roots of y5+11y477y3+132y277y+11=0 are from y=(2u)(1u+u3) where u=t+t1

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