SOLUTION: The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i among its roots. Express f(x) as a product of linear and quadratic polynomials w

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Question 82475: The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i 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):
You can put this solution on YOUR website!
The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
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The real coefficient requirement means -4i must also be a root.
Then:
f(x) = (x+3)(x-4i)(x+4i)
f(x) = (x+3)(x^2+16)
f(x) = x^3+3x^2+16x+48
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Cheers,
Stan H.