SOLUTION: Q:Find a polynomial function of the lowest degree with rational coefficients that has the given numbers as some of its zero radical 3,5i there is a radical sign over the 3, a

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Question 843637: Q:Find a polynomial function of the lowest degree with rational coefficients that has the given numbers as some of its zero
radical 3,5i
there is a radical sign over the 3, and that is 5i not 51
Thank you
Found 2 solutions by Fombitz, richwmiller:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complex root always come on conjugate pairs.
To have rational coefficients, you need another root with -sqrt%283%29 to cancel out the outer and inner terms in the FOIL method.

f%28x%29=%28x-sqrt%283%29%29%28x%2Bsqrt%283%29%29%28x-5i%29%28x%2B5i%29
f%28x%29=%28x%5E2-3%29%28x%5E2%2B25%29
f%28x%29=x%5E4%2B25x%5E2-3x%5E2-75
f%28x%29=x%5E4%2B22x%5E2-75

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
complex solutions are always in pairs
The solutions are +-sqt(3), +-5i
(x-5i)*(x+5i)*(x-sqrt(3))
0 = (sqrt(3)-x) (x^2+25)
0 = x^3-sqrt(3)x^2+25 x-25sqrt(3)
This only has sqrt(3) and not -sqrt(3) as a zero.