SOLUTION: 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 wit

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 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 wit      Log On


   

Question 62538: 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) About Me  (Show Source):
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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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If f(x) has real coefficients and 3+i is a root, then x=3-i is also a root.
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So, f(x)=(x-4)(x-(3+i))(x-(3-i))
f(x)=(x-4)((x-3)^2+1)
f(x)=(x-4)(x^2-6x+10)
Cheers,
Stan H.