anonymous
  • anonymous
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 8, -14, and 3 + 9i f(x) = x4 - 11x3 + 72x2 - 606x + 10,080 f(x) = x4 - 303x2 + 1212x - 10,080 f(x) = x4 - 11x3 - 72x2 + 606x - 10,080 f(x) = x4 - 58x2 + 1212x - 10,080
Mathematics
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SOLVED
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chestercat
  • chestercat
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tkhunny
  • tkhunny
What's your plan? Zero of 8 means a factor of what? Zero of -14 means a factor of what? Zero of 3+9i means what other zero and a factor of what?
anonymous
  • anonymous
i know its going to be (x-8)(x+14) but i dont know what to do with the 3-9i
anonymous
  • anonymous
@tkhunny

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tkhunny
  • tkhunny
The answer to that question is in this hint: "with real coefficients" If 3+9i is a zero, then, just like the others (x - (3+9i)) is a factor. However, if this is all we do, we are NOT going to get Real Coefficients. We need to throw in a Complex Conjugate. Thus, 3-9i must also be a zero and (x-(3-9i)) must also be a factor. Multiply those two and you should get a nice quadratic trinomial with REAL coefficients. This is the deal. If we are to get Real Coefficients, Complex zeros MUST occur in Conjugate Pairs. Simple as that. Make sense?

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