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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Nerdsarecool
  • Nerdsarecool
The answer is
Nerdsarecool
  • Nerdsarecool
If it passes through the origin there is another solution at x = 0. If i is a zero then -i is another zero since complex roots come in conjugate pairs that way. Likewise, if 1-i is a zero then 1 + i is also a zero. Use the factor theorem to convert these five zeros into factors: (x + 0) (x + i) (x - i) (x - 1 + i) (x - 1 - i) Multiply these factors together: x^5 - 2x^4 + 3x^3 - 2x^2 + 2x
mathmale
  • mathmale
Excellent work, Nerd! But next time, let the other person do some of the work, with your guidance. He or she could have multiplied those factors together.

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