SOLUTION: I dont understand "The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3+i among its roots. Express f(x) as a product of linear and qua

Question 65543: I dont understand
"The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3+i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients."

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
"The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3+i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients."
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There are two rules involved:
1. If a is a root, x-a is a factor
2. If a+bi is a root, and all coefficients of f(x) are Real, then a-bi is a root.
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So,
f(x)=(x-4)(x-(3+i))(x-(3-i))
=(x-4)((x-3)-i)((x-3)+i)
=(x-4)((x-3)^2+1)
=(x-4)(x^2-6x+10)
Cheers,
Stan H.
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