anonymous
  • anonymous
Find a polynomial with integer coefficients, with leading coefficient 1, degree 5, zeros i and 3- i, and passing through the origin
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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baru
  • baru
consider an arbitrary degree 5 polynomial \[Ax^5+Bx^4+Cx^3+Dx^2+Ex+F=0\]
baru
  • baru
question says leading co-efficient =1 so A=1
baru
  • baru
\[y=x^5+Bx^4+Cx^3+Dx^2+Ex+F\] actually consider this

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baru
  • baru
(0,0) is a point on it. substitute and get F=0
baru
  • baru
\[y=x^5+Bx^4+Cx^3+Dx^2+Ex+0\]
baru
  • baru
well now you have 4 unknowns, and you are given 2 roots. subsitute them, and eliminate 2 of the unknowns, i guess there is no unique answer to this problem, you can choose what ever you want for the remaining variables
baru
  • baru
sorry ignore that, i just read up something conjugate root theorem: if a+bi is a root, then a-bi is also a root
baru
  • baru
so you actually have roots : i, -i, 3-i, 3+i four roots and four unknowns

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