anonymous
  • anonymous
PLEASE HELP!!!!!!!!!!!! Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 2, -4, and 1 + 3i
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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DecentNabeel
  • DecentNabeel
Given zeros: 2, -4, and -1 + 3i, -1 - 3i has to be another zero since complex zeros come in pairs and -1 - 3i is the complex conjugate of -1 + 3i. You get the polynomial: f(x) = (x - 2)(x + 4)(x - (-1 + 3i))(x - (-1 - 3i))
anonymous
  • anonymous
but the answers they give me are f(x) = x4 - 2x2 + 36x - 80 f(x) = x4 - 3x3 + 6x2 - 18x + 80 f(x) = x4 - 9x2 + 36x - 80 f(x) = x4 - 3x3 - 6x2 + 18x - 80 @DecentNabeel
DecentNabeel
  • DecentNabeel
Since polynomial has real coefficients, and one zero = 1+3i, then another zero must be its conjugate: 1−3i Zeros: 2, −4, 1+3i, 1−3i P(x) = (x−2) (x+4) (x−(1+3i)) (x−(1−3i)) P(x) = (x−2) (x+4) ((x−1)−3i) ((x−1)+3i) P(x) = (x−2) (x+4) ((x−1)²−9i²) P(x) = (x−2) (x+4) ((x²−2x+1)+9) P(x) = (x−2) (x+4) (x²−2x+10) P(x) = (x² + 2x − 8) (x² − 2x + 10) P(x) = x⁴ − 2x³ + 10x² + 2x³ − 4x² + 20x − 8x² + 16x − 80 P(x) = x⁴ − 2x² + 36x − 80

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DecentNabeel
  • DecentNabeel
first option is the answer @nanaruiz123
DecentNabeel
  • DecentNabeel
are you understand @nanaruiz123
anonymous
  • anonymous
ohh okay thank you so much @DecentNabeel
DecentNabeel
  • DecentNabeel
no problem :)

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