Question 1172003: A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over ℝ.
−2, 0, 4 + i; degree 4
f(x) =
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! if 4+i is a root, then 4-i is a root, since complex roots are conjugate.
two of the factors are (x+2) and x
The other two are from (x-4-i) and (x-4+i)
If we multiply those factors together, we get
x^2-4x+ix-4x+16+4i-ix+4i-i^2=x^2-8x+17
The factors are x, (x+2), and x^2-8x+17.
f(x) is their product, or x(x+2)(x^2-8x+17)
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