decemberlove860 decemberlove860
  • 23-03-2017
  • Mathematics
contestada

P(x)= P has degree 3 and zeros 5 and i.

Respuesta :

jdoe0001 jdoe0001
  • 23-03-2017
keeping in mind that complex solutions never come all by their lonesome, they always come with their sister

thus, "i" is not there all by herself, her sister is there too, namely the conjugate

so
i = 0+i     and thus its conjugate sister will be  0-i

thus    [tex]\bf \begin{cases} x=5\to &x-5=0\\ x=0+i\implies x=i\to &x-i=0\\ x=0-i\implies x=-i\to &x+i=0 \end{cases} \\\\\\ (x-5)(x-i)(x+i)=\textit{original polynomial}[/tex]
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