Question 1049443: The problem I'm stuck on is:
Given the zeros, -4, 5, -2, -√14, -2i; write a polynomial function or least degree that has rational coefficients.
The part I'm stuck on is the roots -2i and -√14. I know that I need to use the quadratic equation to figure out that part of the equation. Also, I remember that for the others I need to write out:
(x+4)(x-5)(x+2)
I'm really struggling with this one so help would be very appreciated!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Given the zeros, -4, 5, -2, -√14, -2i; write a polynomial function or least degree that has rational coefficients.
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To arrive at rational coefficients -sqrt(14) must be paired with +sqrt(14)
and +2i must be paired with -2i.
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Then:
f(x) = (x+4)(x-5)(x+2)(x+sqrt(14))(x-sqrt(14)(x+2i)(x-2i)
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f(x) = (x+4)(x-5)(x+2)(x^2-14)(x^2+4)
etc.
Cheers,
Stan H.
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