How do you write a polynomial equation of least degree given the roots 6, 2i, -2i, i, -i?

1 Answer
Sasha P.
Apr 23, 2017

z^5-6z^4+5z^3-30z^2+4z-24=0z5−6z4+5z3−30z2+4z−24=0

Explanation:

(z-6)(z-2i)(z-(-2i))(z-i)(z-(-i))=0(z−6)(z−2i)(z−(−2i))(z−i)(z−(−i))=0
(z-6)(z-2i)(z+2i)(z-i)(z+i)=0(z−6)(z−2i)(z+2i)(z−i)(z+i)=0
(z-6)(z^2-2zi+2zi-4i^2)(z^2-zi+zi-i^2)=0(z−6)(z2−2zi+2zi−4i2)(z2−zi+zi−i2)=0
(z-6)(z^2+4)(z^2+1)=0(z−6)(z2+4)(z2+1)=0
(z-6)(z^4+4z^2+z^2+4)=0(z−6)(z4+4z2+z2+4)=0
(z-6)(z^4+5z^2+4)=0(z−6)(z4+5z2+4)=0
z^5-6z^4+5z^3-30z^2+4z-24=0z5−6z4+5z3−30z2+4z−24=0

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