Posted by **Hailey** on Wednesday, March 27, 2013 at 8:09am.

Form a polynomial f(x) with real coefficients having the given degree and zeros.

Degree 5;

Zeros: -3; -i; -6+i

F(x)=a ( )

- Form a polynomial f(x) -
**Reiny**, Wednesday, March 27, 2013 at 9:29am
Complex numbers always appear as conjugate pairs, so if you have -i, then you also have +i

and if you have -6+i, there will also be -6 - i

so we know we have factors of (x+3) , (x^2 + 1) and two more

I will use the sum and product rule to find the other

sum of -6+i and -6 - i = -12

product of the above is 36 - i^2 = 36 + 1 = 37

resulting in the quadratic factor

x^2 + 12x + 37

You could also expand (x -(-6+i))(x - (-6-i)) and get the same result

so f(x) = (x+3)(x^2 + 1)(x^2 + 12x + 37)

notice, if expanded this will give you a 5th degree polynomial. If you have to expand it, do it very carefully and patiently.

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