SOLUTION: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -3, -2+i f(x)= ?

Question 677325: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.
-3, -2+i
f(x)= ?
Answer by aaronwiz(69) (Show Source): You can put this solution on YOUR website!
Hi, I am in 10th grade honors trig and pre calc, and I will do my best to help you.
the key to this problem is that it sates it has real coef. This allows us to use the complex conjugates thm. which states if a polynomial has real coef and a+bi is a factor then a-bi (the conjugate) is also a factor.
We can apply this to your problem since it has real coefficients we know -2-i is also a factor. We now know all three zeros of the polynomial.
According to the factor thm. we can say f(x)=(x+3)(x-(-2+i))(x-(-2-i))
You can leave it in this form if your teacher wants it factored down to the linear factors. However it is usually much better to get rid of the imaginary numbers, by turning it into a irreducible quadratic....
f(x)=(x+3)(x+2-i)(x+2+i)
so
f(x)=(x+3)(x^2+4x+5)
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